
Glass TcJ 1 l : 
Book t- 



/ 



THE 

AND 

ENGINEER'S PRACTICAL GUIDE: 

CONTAINING 

A CONCISE TREATISE 

ON THE NATURE AND APPLICATION OF MECHANICAL FORCES; ACTION 

OF GRAVITY; THE ELEMENTS OF MACHINERY; RULES AND 

TABLES FOR CALCULATING THE WORKING EFFECTS OF 

MACHINERY; OF THE STRENGTH, RESISTANCE, 

AND PRESSURE OF MATERIALS ? WITH 

TABLES OF THE WEIGHT AND COHE- . 

SIVE STRENGTH OF IRON 
AND OTHER METALS. 

COMPILED AND ARRANGED 

BY THOMAS V KELT, 

OF THE " GLOUCESTER CITY MACHINE COMPANY," N. J. 

2To fofjtri) is atftetJ 

VALUABLE HINTS TO THE YOUNG MECHANIC ON THE CHOICE 

OF A PROFESSION; MISDIRECTION OF INDUSTRY; 

INTELLECTUAL CULTIVATION, AND THE 

STUDIES AND MORALS OF THE 

MECHANIC, ETC., ETC. 

BY JOHN FROST, LL. D. 



BOSTON: 

CROSBY & AINSWORTH. 

NEW YORK: OLIVER S. FELT. 

1866. 







. 


Entered, 


according to Aet of Congress 


in the year 1866, by 




CROSBY & AINSWORTH, 


In the Clerk's Office of the District Court of the District of Massachusetts. 










STEREOTYPED AT 


THE 


BOSTON STEREOTYPE 


FOUNDRY, 




4 SPRING LANI 

> 


> 


• 


v • 




,. 




■« 



CONTENTS, 



PRACTICAL GEOMETRY. 
nieorems. Page 

To erect a perpendicular on a right line, „ 9 

To erect a perpendicular at the end of a line, 9 

To bisect a given angle, 10 

To describe a circle through three given points out of a 

right line, « 10 

To find the centre of a given circle, 11 

To fine! the length of any given arc of a circle, 11 

To draw a tangent to a circle, 11 

To draw lines toward the centre* of a circle, the centre 

being inaccessible,. 11 

To describe the segment of a circle, 12 

To describe an ellipse, or oval, 13 

To describe an elliptic arch, 13 

To describe a parabola, . 14 

To measure an intercepted line, 14 

To find the distance between two inaccessible objects, . 15 

To design a beam of strongest section, 15 

• To obtain the distance of an inaccessible object, 16 

To find the proper position for the eccentric in a steam- 
engine, - . . . . 16 

To find the length of valve-levers, 16 

To define the throw of au eccentric, 17 

To describe any regular polygon, 17 

To coustruct a square upon a right line, . 18 

To form a square equal to a given triangle, 18 

To form a square equal to a given rectangle, 18 

To form a rectangle equal to a given square, 18 

To bisect any given triangle, 19 

To describe a circle in a given triangle, 19 

To form a rectangle in a given triangle, ......... 19 



CONTENTS. 



DECIMAL ARITHMETIC. 

Definitions, 20 

Reduction, 20 

Definitions of Arithmetical Signs, 24 

Decimal Approximations, 25 

Decimal Equivalents, 26 

MENSURATION. 

Mensuration of Surfaces. 

To measure the surface of a square, rectangle, and 
rhomboid, 27 

Triangles. 

Two sides of a triangle given, to find the third,. ... 28 

To find the area of a triangle, 29 

When only the three sides of a triangle can be given, to 
find the area, 30 

Polygons. 

Table of polygons, 31 

The Circle and its Sections. 

Observations and definitions, 32 

General rules in relation to the circle, 33 

To find the diameter of a circle, when any chord and 

versed sine are given, . . - 34 

To find the length of any given arc of a circle, 34 

To find the area of the sector of a circle, 35 

To find the area of a circular ring, ................... 35 

To find the area of an ellipse, • 36 

To find the area of a parabola, 36 

Mensuration of the Superficies, Solidities, and Capacities of 
Bodies. 
To find the solidity or capacity of cubical figures,. ... 37 
To find the convex surface and solidity of a cylinder, . . 38 

To find the length of any cylindrical heliX; 39 

To find the convex surface and solidity of a cone, ... 39 
To find the solidity or capacity of any frustum of a cone 

or pyramid, 40 

To find the solid contents of a wedge, 41 

To find the convex surface, the solidity, or the capacity, 
of a sphere or globe, . . . 41 



CONTENTS* 



INSTRUMENTAL ARITHMETIC. 

Explanation of the Slide Rule, . . ........ 43 

Numeration,, 44 

To multiply by flie Slide Rule, ................ 44 

To divide by the Slide Rule, . 44 

■Proportion, 45 

Rule of TJiree inverse,. ................... 45 

Square and Cube Roots. 

To find the geometrical mean proportion between two 

numbers, .................. 46 

Mensuration of Surface. 

Squares, rectangles, &c, .............. . . 47 

Circles, polygons, &c, ................. 47 

Tables of Gawge- Points for the Slide Rule, . » 48 

Mensuration of Solidity and Capacity, 48 

Land Surveying, . .„» ........ . 50 

Power of Steam- Engines. 

Condensing engines, «........»., 50 

Non-condensing engines, 50 

Of Engine Boilers, 51 

STRENGTH OP MATERIALS. 

Definitions, 51 

Table of Tenacities, Resistance to Compression, and other 

Properties of Materials of Construction, ......... 52 

Table of Comparative Strength and Weight of Ropes and 

Chains, 53 

Table of Metallic Alloys, .................. M 

Resistance of Bodies to Lateral Pressure, 54 

Table of Practical Data, .................. 54 

To find the dimensions of a beam capable of sustain- 
ing a given weight, 55 « 

To determine the absolute strength of a rectangular 

beam of timber, .................... 55 

To determine the dimensions of a beam with a given de- 
gree of deflection, 56 

To find the absolute strength of a beam fixed at one 

end, and loaded at the other, . 57 

Cast iron beams of strongest section, 57 

Of wooden beams trussed, 58 

To find the absolute strength of cast iron beama, . ... 58 
1 






t> CONTENTS. 

Table of Dimensions for Cast Iron Beams, ...*,«., y 59 

To find the weight of a cast iron beam, 60 

Resistance of Bodies to Flexure by Vertical Pressure,. ... 60 
To determine the dimensions of a column to bear a 

given pressure, .................... 61 

Table of Dimensions of Cylindrical Columns of Cast Iron, . 62 

Resistance of Bodies to Twisting, .............. 6? 

Relative strength of metals to resist torsion, ...... 64 

MECHANICS. 

Preliminary Remarks, * . . . . 64 

The Lever, ......................... 65 

The Wheel and Axle, or Crane. 

To determine the amount of effective power produced 

from a given power, by a crane, ............ 67 

Two parts of a crane given, to find the third, , 68- 

The Pulley, 6S 

Table of Inclined Planes, .................. 70 

Example of Incline and Velocity, ............ 71 

The Wedge, , 72 

The Screw, ... ................ . 73- 

CONTINUOXJS CIRCULAR MOTION. 

When Time is not taken into Account. 

To find the number of revolutions of the last, to one of 
the first, in a train of wheels and pinions,. ...... 75 

When Time must he regarded. 

The distance between the centres and velocities of two 
wheels given, to find their diameters, ......... 76 

To determine the proportion of wheels for screw-cutting 

by a lathe,. 77 

Table of Change- Wheels for Screw-cutting, 80 

Table of the Pitch of Small Wheels, ............. 81 

Table of the Strength of Teeth of Cast Iron Wheels, .... 81 

PRACTICAL PROPERTIES O^ WATER. 

Effects produced by Water in its natural State, 82 

To find the velocity of water issuing a circular orifice at 
any given depth from the surface, ........... 83 ; 



CONTENTS. 



STEAM POWEE. 

To estimate the amount of advantage gained by using 

steam expansively in a steam-engine, . 88 

Effects produced by Water in an aeriform State, ...... 90 

Table of the Elastic Force of Steam, ............ 91 

Table of Boiling Points, ....... 93 

Elastic Force of Steam in Inches of Mercury, 4 93 

Effects produced by Air, . . . . ...... 93 

Table of the Expansion of Atmospheric Air by Heat, .... 94 

Table of the Quantity of Water in Pumps, . . . . 95 

Table of Force and Common Appellations of Winds, . . < . 97 

FRICTION*. 

Laws of Friction, 98 

BOILERS MD THE STEAM-ENGINE. 

Construction of Boilers, 100 

To determine the proper quantity of heating surface 

in a boiler, 101 

To determine the proper dimensions for a wagon- 
shaped boiler, 102 

To determine the dimensions for a cylindrical boiler, . 102 

Specified Particulars, 103 

Heating Powers of Combustible Substances, ........ 103 

Tables of Dimensions for Cylinders, 104 

PROPERTIES OF BODIES. 

Tables of the Specific Gravities of Bodies, . .105-107 

PRACTICAL TABLES. 

Weight of Square, Round, and Flat Bar Iron, 110^120 

Proportional Breadths for six-sided Nuts for Bolts, . . . . 130 

Weights of Sheet Iron, Copper, and Brass, 131 

Comparative Weights of different Bodies, 132 

Weights of Pipes of various Metals, < 133 

Weight of Cast Iron Balls, 134 

Mensuration of Timber. 

Flat or board measure, 135 

Cubic or solid measure, 136 



O CONTENTS. 

Cast Metal Cylinders, 137 

Cast Iron Pipes, 138 

Compositions of Copper, Tin, and Zinc, . . i . * 139 

Degrees of Heat, i . . . . ........ i . 139 

LOGAKITHMS. 

Utility of Logarithmic Tables, ♦ * . . . . ; . . 146 

To find the logarithm of any whole number under 100, . 147 
To find the logarithm of any number between 100 and 

1000, 147 

To find the number indicated by a logarithm,. ..... 148 

Table of Logarithms from 1 to 100, 150 

MISCELLANEOUS. 

Centres, 140 

Cohesion,. .......... i ............ i . 141 

Case- Hardening, 141 

Steam Engines. 

To estimate the effective power of ah engine, 143 

To determine the proper velocity for a piston, 143 

Table of approximate velocities for pistons, 144 

Parallel motion in a steam-engine, 144 

Table of distances for a parallel motion, 145 

Table of the Quantity and Weight of Water in Pipes, . . ; 151 

Changes induced in the Structure of Iron, 152 

Strength of Journals of Shafts, 156 

Journals of First Movers, 158 

Strength of Wheels, 160 

Tables of Circumferences and Areas of Circles, . . . . 163-171 

Square and Cube Roots of Numbers, 172 

Varnishes, 173 

Solders, 176 

Capacity of Cisterns, 177 

Screws, 177 

Weights of various Substances, 178 



CONTENTS, 



PART SECOND. 



INTRODUCTION. 

PAGE 

Choice of a Profession. — Respectability of Mechanical 

Trades, 179 

CHAPTER I. 

The Mechanic should be Master of his Trade, 186 

CHAPTER II. 
The Mechanic should remain attached to his Trade, .... 193 

CHAPTER III. 
The Mechanic should honor his Trade, 200 



CHAPTER IV. 

The Mechanic should devote his Leisure to the General 

Interests of his Trade, . 214 

CHAPTER V. 

Misdirection of Industry. — Prejudices against the Me- 
chanical Trades, 216 



CHAPTER VI. 

Intellectual Cultivation of the Mechanic. — ■ Its Impor- 
tance, 222 



10 CONTENTS. 

CHAPTER VII. 

Means of Intellectual Cultivation accessible to the Me- 
chanic, 240 

CHAPTER VIII. 

Eewards of Intellectual Cultivation accessible to the Me- 
chanic, . 247 

CHAPTER IX. 
The Mechanic's Studies, 250 

CHAPTER X. 

The Mechanic's Studies continued, 266 

CHAPTER XI. 
The Mechanic's Studies continued, 329 

CHAPTER XII. 
The Mechanic's Studies continued, 340 

CHAPTER XIII. 
The Mechanic's Studies continued, .....* 359 

CHAPTER XIV. 
The Morals of the Mechanic, 381 



THE WORKSHOP COMPANION. 



'PRACTICAL GEOMETRY. 



X* 



Geometry is the science which investigates and 
demonstrates the properties of lines on surfaces and 
solids ; hence, Practical Geometry is the method 
of applying the rules of the science to practical pur- 
poses. 

1, From any given point {in a straight line, to erect 
a perpendicular ; or, to make a line at right angles 
with a given line. 

On each side of the point A, from 
which the line is to be made, take 
equal distances, as A b, A c ; and 
from b and c as centres, with any - — ^ — f- 
distance greater than b A, or c A, h ; c 
describe arcs cutting each other at 
d ; then will the line A d be the per- \J^ 

pendicular required. ' \ 

2. When a perpendicular is to be made at or near 
the end of a given line. 

With any convenient radius, and 
with any distance from the given line 
A 6, describe a portion of a circle, as 
b A c, cutting the given point in A ; 
draw, through the centre of the circle 
n, the line b n c; and a line from the 
point A, cutting the intersections at c, 
is the perpendicular required. 




10 



PRACTICAL GEOMETRY, 



3. To do the same otherwise. 

From the given point A, with, 
any convenient radius, describe the 
arc deb; from d, cut the arc in c, 
and from c f cut the arc in b ; also, 
from c and 6 as centres, describe 
arcs cutting each other in t ; then 
will the line A i be the perpen- 
dicular as required. 




Note. — ■ When the three sides of a triangle are in the pro- 
portion of 3, 4, and 5 equal parts, respectively, two of the 
sides form a right angle ; and observe that in eaeh of these 
or the preceding problems, the perpendiculars may be con- 
tinued below the given lines, if necessarily required. 

4. To bisect any given angle. 

From the point A as a centre, with v ^T? 

any radius less than the extent of the \ ' / 

angle, describe an arc, as c d ; and \ / 

from c and d as centres, describe arcs y- J 

cutting each other at b ; then will °\ / 
the line A b bisect the angle as re- \ / 

quired. Nr 

5. To Jind the centre of a circle, or radius, thai 
shall cut any three given points, not in a direct line. 

From the middle point b as a 
centre, with any radius, as b c, b d, 
describe a portion of a circle, as 
c s d ; and from r and t as centres, 
with an equal radius, cut the por- 
tion of the circle in c s and d s ; j 
draw lines through where the arcs 
cut each other ; and the intersec- 
tion of the lines at s is the centre 
of the circle as required. 




PRACTICAL GEOMETRY. 



11 





6. To find the centre of a given 
circle. 

Bisect any cord in the circle, as 
A B, by a perpendicular, C D ; bi- 
sect also the diameter E D in /; 
and the intersection of the lines at 
f is the centre of the circle re- 
quired. 

7. To find the length of any given 
arc of a circle. 

With the radius A C, 
equal to ^th the length of 
the chord of the arc A B, A 
and from A as a centre, 
cut the arc in c ; also from B as a centre, with equal 
radius, cut the chord in b ; draw the line C b ; and 
twice the length of the line is the length of the arc 
nearly. 

8. TJirough any given point, to draw a tangent to 
a circle. • 

Let the given point be at A ; 
draw the line A C, on which 
describe the semicircle ADC; 
draw the line A D B, cutting the 
circumference in D, which is the 
tangent as required. 



9. To draw from or to the circumference of a cir- 
cle lines tending towards the centre, when the centre 
is inaccessible. 

Divide the whole or any given portion of the cir- 
cumference into the desired number of equal parts ; 
then, with any radius less than the distance of two 
2 




12 



PRACTICAL GEOMETRY. 




divisions, describe arcs cutting each other, as A 1, 

B 1, C 2, D 2, &c. ; 

draw the lines C 1, 

B 2, D 3, &c, which 

lead to the centre as 

required. 

To dfaw the end lines. 

As A r, F r, from C describe the arc r, and with 
the radius C 1, from A or F as centres, cut the former 
arcs at r, or r, and the lines A r, F r, will tend to the 
centre as required. 

10. To describe an arc, or segment of a circle, of 
large radii. 

Of any suitable material, construct a triangle, as A 
B C ; make A B, B C, each equal in length to the 
chord of the arc D E, and height, twice that of the arc 




B b. At each end of the chord D E fix'a pin, and at 
B, in the triangle, fix a tracer, (as a pencil,) move the 
triangle along the pins as guides ; and the tracer will 
describe the arc required. 

11. Or otherwise. 

Draw the chord A C B ; also draw the line H D 
I, parallel with the 
chord, and equal to 
the height of the 
segment ; bisect the 
chord in C, and 
erect the perpen- 
dicular C D ; join A D, D B ; draw A H perpendicular 
to A D, and B I perpendicular to B D, erect also the 
perpendiculars A n, B n ; divide A B and H I into any 



I 


2 3 


3> 3 2 n 1 


1 


W\ 


^# 


1 


L 1 2 3 


C 3 2 1 B 



PRACTICAL GEOMETRY. 



13 




number of equal parts; draw the lines 1 1, 2 2, 3 3, 
&c. ; likewise divide the lines A n, B n, each into half 
the number of equal parts ; draw lines to D from each 
division in the lines An,B n, and, through where they 
intersect the former lines, describe a curve, which will 
be the arc or segment required. 

12. To describe an ellipse, having the two diameters 
given. 

On the intersection of the * 

two diameters as a centre, with 
a radius equal to the difference 
of the semi-diameters, describe 
the arc a b ; and from b as a 
centre, with half the chord b c a, 
describe the arc c d ; from o, as 
a centre, with the distance o d, T 

cut the diameters in dr,di ; draw the lines r, s, s, and 
t, s, s ; then from r and t describe the arcs s, s s s, s ; 
also from d and d, describe the smaller arcs s, s, s, s, 
which will complete the ellipse as required. 

13. To describe an elliptic arch, the width and rise 
of span being given. 

Bisect with a line at right 
angles the chord or span A . 
B ; erect the perpendicular A « 
q, and draw the line q D L 
equal and parallel to A C ; 
bisect A C and A q in r and 
n ; make C I equal to C D, 
and draw the line I r q ; draw 
also the line n s D ; bisect s 
D with a line at right angles, 
and meeting the line C D in 
g ; draw the line g q, make C P equal to C k, and draw 
the line g P i ; then from g as a centre, with the radius 
g D, describe the arc s T> i ; and from k and P as cen- 
tres, with the radius A k, describe the arcs A s and B 
i, which completes the arch as required. Or, 




14 



PRACTICAL GEOMETRY. 



14. Bisect the chord A B, and fix at right angles any 
straight guide, as b c ; pre- 
pare, of any suitable mate- 
rial, a rod or staff, ecfual to 
half the chord's length, as 
d ef; from the end of the 
staff, equal to the height 
of the arch, fix a pin e, 
and at the extremity a 
tracer f ; move the staff, 
keeping its end to the 
guide and the fixed pin to the chord 5 and the tracer 
will describe one half the arc required. 

15. To describe a parabola, the dimensions being 
given. 

Let A B equal the length, and C D the breadth of 
the required parabola ; divide C A, C B into any num- 

3 





a. 1 a 3 c 8 a I 

ber of equal parts ; also divide the perpendiculars A a 
and B b into the same number of equal parts ; then 
from a and b draw lines meeting each division on the 
line A C B ; and a curve line drawn through each in- 
tersection will form the parabola required. 

16. To obtain by measurement the length of any 
direct line, though intercepted by some material object. 

Suppose the 
distance be- 
tween A and B a d 

*is required, but 
the right line is 
intercepted by 
the object C. 
On the point d, 
with any con- 




PRACTICAL GEOMETRY, 



15 



venient radius, describe the arc c c, make the arc twice 
the radius in length, through which draw the line dee, 
and on e describe another arc equal in length to once 
the radius, as eff; draw the line efr equal to ef d ; 
on r describe the arc j j, in length twice the radius ; 
continue the line through r j, which will be a right 
line, and d e, or e r, equal the distance between d r 
by which the distance between A and B is obtained as 
required; 

Hi. A round piece of timber being given, out of 
which to cut a beam of strongest section. 

Divide into three equal parts any 
diameter in the circle, as A d, e C ; 
from d or e, erect a perpendicular 
meeting the circumference of the 
circle, as d B ; draw A B- and B C, 
also A D equal to B C, and D C equal 
to A B, and the rectangle will be a 
section of the beam as required. 

18. To measure the distance between two objects, 
both being inaccessible. 

From any point C draw A 
any line C c, and bisect it 
in JD ; take any point E in 
the prolongation of A C, and 
draw the line E e, making 
D e equal to D E ; in like 
manner take any point F in 
the prolongation of B C, and 
make D / equal to F D. 
Produce A D and e c till 
they meet in a, and also B 
D and f c till they meet in 
b ; then a b equal A B, or 
the distance between the 
objects as required. 
2* 





-a*-,.- -,-<r ^- 



16 



PRACTICAL GEOMETRY. 




19. To ascertain the distance, geometrically , of any 
inaccessible object on an equal plane. 

Let it be required to find the 
distance between A and B, A 
being inaccessible; produce the 
line in the direction of A B to 
any point, as D 5 draw the line D 
d at any angle to the line A B \ 
bisect the line D d, through which 
draw the line B 6, making c b 
equal to B c ; draw the line dba; 
also through c, in the direction c 
A, draw the line a c A, intersect- 
ing the line dba; then b a equal 
B A, the distance required. 

20. Otherwise. 
Prolong A B to any po'int 

D, making B C equal to C 
D ; draw the line D a at any 
angle with D A, and the line 
C 6 similar toBc; draw also 
the line D E F, which inter- 
sects the line D a ; then a b 
equal B A, or the distance 
required. 

21 . To find the proper position for an eccentric, in 
relation to the crank in a steam engine, the angle of 
eccentric rod, and travel of the valve, being given. 

Draw the right line A 
B, as the situation of the 
crank at commencement 
of the stroke ; draw also 
the line C d, as the proper 
given angle of eccentric 
rod with the crank ; then 
from C as centre, describe 
a circle equal to the travel 
of the valve ; draw the line ef at right angles to the line 





PRACTICAL GEOMETRY. 



17 




C a, draw also the lines 1 1, and 2 2, parallel to the line 
ef; and at a distance from ef on each side, equal to the 
tap and lead of the valve, draw the angular lines C 1, 
C 2, which are the angles of eccentric with the crank, 
for forward or backward motion, as may be required. 

22. The throw of an eccentric, and the travel of the 
valve in a steam-engine, also the length of one lever 
for communicating motion to the valve, being given, 
to determine the proper length for the other. 

On any right line, as A B, describe a circle A D 
equal to the throw 
of eccentric and 
travel of valve ; 
then from C as a 11 
centre, with a ra- 
dius equal to the 
length of lever a 

given, cut the line A B, as at d, on which describe a 
circle, equal to the throw of eccentric or travel of valve, 
as may be required j draw the tangents B a, B a, cut- 
ting each other in the line A B, and d B is the length 
of the lever as required. 

Xote.— -The throw of an eccentric is equal to the sum of 
twice the distance between the centres of 
formation and revolution, as a b, or to the 
degree of eccentricity it is made to describe, 
as c d. And 

The travel of a valve is equal to the sum of 
the widths of the two steam openings, and 
the valve's excess of length more than just 
sufficient to cover the openings. 

23. To inscribe any regular polygon in a given circle. 
Divide any diameter, as A B, into 

so many equal parts as the polygon is 
required to have sides ; from A and B 
as centres, with a radius equal to the 
diameter, describe arcs cutting each 
other in C ; draw the line CD through 
the second point of division on the 
diameter e, and the line D B is one 
side of the polygon required. 





18 



PRACTICAL GEOMETRY. 





24. To construct a square upon a given right line. 

From A and B as centres, 
with the radius A B, describe 
the arcs A c b, B c d, and from 
c, with an equal radius, describe 
the circle or portion of a circle 
e d, A B, b c ; from b d cut the 
circle at e and. c , k draw the 
lines A e, B c, also the line 5 1, 
which completes the square as 
required. 

25. To form a square equal in area to a given 
triangle. 

Let A B C be the given tri- 
angle ; let fall the perpendicu- 
lar B d, and make A e half the 
height d B j bisect e C, and de- 
scribe the semicircle e n C ; 
erect the perpendicular A s, or 
side of the square, then A s t x is the square of equal 
area as required. 

26. To form a square equal in area to a given rec- 
tangle. 

Let the line A B equal the length and breadth of 
the given rectangle ; bisect the 
line in e, and describe the semi- 
circle A D ' B ; then from A 
with the breadth, or from B 
with the length, of the rec- 
tangle, cut the line A B at C, 
and erect the perpendicular C D, meeting the curve at 
IX and C D equal a side of the square required. 

27. To find the length for a rectangle whose area 
shall be equal to that of a given square, the breadth 
of the rectangle being also given. 

Let A B C D be the given square, and D E the given 
breadth of rectangle ; continue the line B C to F, and 




PRACTICAL GEOMETRY. 



19 



d f a 


^''' 






^'" 


c ^"'' * 



draw the line D F ; also, 
continue the line D C 
to g, and draw the line 
A g parallel to D F ; 
from the intersection of 
the lines at g, draw the 
line g d parallel to D E, 
and E d parallel to D 
g ; then E D d g is the 
rectangle as required, 

28. To bisect any given triangle. 

Suppose ABC the given triangle ; 
bisect one of its sides, as A B in e, 
from which describe the semicircle 
A r B ; bisect the same in r, and 
from B, with the distance B r, cut 
the diameter A B in v; draw the 
line v y parallel to A C, which will 
bisect the triangle as required. 



29. To describe a circle of greatest diameter in a 
given triangle. 

Bisect the angles A and B, and draw the intersecting 
lines AD, B D, cutting 
each other in D ; then from 
D as centre, with the dis- 
tance or radii D C, de- 
scribe the circle C e f, as 
required. 

30. To form a rectangle of greatest 
surface, in a given triangle. 

Let A B C be the given triangle ; 
bisect any two of its sides, as A B, B 
C, in e and d ; draw the line e d; also 
at right angles with the line e d, draw 
the lines e p, dp, and epp d is the rec- 
tangle required. 






20 

DECIMAL ARITHMETIC. 

Decimal Arithmetic is the most simple and ex- 
plicit mode of performing practical calculations, on 
account of its doing away with the necessity of frac- 
tional parts in the fractional form, thereby reducing 
long and tedious operations to a few figures arranged 
and worked in all respects according to the usual rules 
of common arithmetic. 

Decimals simply signify tenths ; thus, the decimal of 
a foot is the tenth part of a foot, the decimal of that 
tenth is, the hundredth of a foot, the decimal of that 
hundredth is the thousandth of a foot, and so might the 
divisions be carried on and lessened to infinity ; but in 
practice it is seldom necessary to take into account any 
degree of less measure than a one-hundredth part of 
the integer or whole number. And, as the entire system 
consists in supposing the whole number divided into 
tenths, hundredths, thousandths, &c, no peculiarity of 
notation is required, otherwise than placing a mark or 
dot, to distinguish between the whole and any part of 
the whole ; thus, 34*25 gallons signify 34 gallons 2 
tenths and 5 hundredths of a gallon ; 11*04 yards sig- 
nify 11 yards and 4 hundredths of a yard, 16*008 shil- 
lings signify 16 shillings and 8 thousandth parts of a 
shilling ; iom which it must appear plain, that ciphers 
on the right hand of decimals are of no value whatever ; 
but placed on the left hand, they diminish the decimal 
value in a tenfold proportion, — for *6 signify 6 tenths ; 
•06 signify 6 hundredths ; and *006 signify 6 thou- 
sandths of the integer, or whole number. 

REDUCTION. 

Reduction means the construing or changing of vul- 
gar fractions to decimals of equal value ; also finding 
the fractional value of any decimal given. 

Rule 1. Add to the numerator of the fraction any 
number of ciphers at pleasure, divide the sum by the 
denominator, and the quotient is the decimal of equiva- 
lent value. 



DECIMAL ARITHMETIC. 



21 



Rule 2. Multiply the given decimal by the various 
fractional denominations of the integer, or whole num- 
ber, cutting off" from the right hand of each product, for 
decimals, a number of figures equal to the given number 
of decimals, and thus proceed until the lowest degree, 
or required value, is obtained. 

Ex. 1. Required the decimal equivalent, or decimal 
of equal value, to T 3 2 of a foot. 

3^0 — -25, the decimal required. 

Ex. 2. Reduce the fraction \ of an inch to a deci- 
mal of equal value. 

ujlqj — -125, the decimal required. 

Ex. 3. What is the decimal equivalent to -| of a 
gallon ? 

li^oo — -875, the decimal equivalent. 

Ex. 4. Required the fractional value of the decimal 
•40625 of an inch. 

•40625 
Multiply by \ 8 

3-25000 

X^l ? 

•50000 

XA=A ? 

J/00000 I and ^ of an inch, the value 
~ required. 

Ex. 5. What is the fractional value of '625 of a 
cwt. ? 

•625 
Multiply by 4 qrs. 4 

2-500 
X 28 lbs. 28 

14-000 — 2 quarters and 14 lbs., the 
value required. 



22 DECIMAL ARITHMETIC. 

Ex. 6. Ascertain the fractional value of # 875 of an 
imperial gallon. 

•875 
Multiply by 4 quarts 4 

3-500 
X 2 pints 2 

1-000 = 3 quarts and 1 pint, the 
id. 



value requirec 

Ex. 7. What is the fractional value of -525 of a £. 
sterling ? 

•525 
Multiply by 20 sh. 20 

10-500 
X 12 pence 12 

6-000 — 10 shillings and 6 pence, 
the value required. 

Independent of the mark or dot which distinguishes 
between integers and decimals, the fundamental rules, 
viz., Addition, Subtraction, Multiplication, and Division, 
are in all respects the same as in Simple Arithmetic ; 
and an example in each, illustrative of placing the 
separating point, will no doubt render the whole system 
sufficiently intelligible, even to the dullest capacity. 

Ex. 1. Add into one sum the following integers and 
decimals. 

16-625; 11-4; 20-7831; 12-125; 8-04; and 7*002. 
16-625 
11-4 
, 20-7831 

1 12-125 

8-04 
7-002 

75-9751 = the sum required. 



DECIMAL AEITHMETIC 23 

Ex, 2. Subtract 119-80764 from 234-98276. 
234-98276 
119-80764 

115*17512 = the remainder required* 

Ex. 3. Multiply 62-10372 by 16-732. 

62-10372 x 

16-732 

12420744 
18631116 
43472604 
37262232 
6210372 



1039*11944304 — the product required. 



Observe that the number of figures in the product 
from the right hand, accounted as decimals, are equal 
to the number of decimals in the multiplier and mul- 
tiplicand taken together. 

Ex* 4. Divide 39-375 by 9.25. 
9-25) 39-375 (4-256= the quotient required, 
3700 

2375 Observe that the number of deci- 

1850 mals, in the divisor and quotient 

koIa together, must be equal to the 



4625 

6250 
5550 

700 



number in the dividend. 



iVbte.— The operation might he still continued, so as to 
reduce the quotient to a degree of greater exactitude ; hut 
in practice it is quite unnecessary, being even now reduced 
to a measure of greater nicety than is commonly required* 

3 



24 



DECIMAL ARITHMETIC- 



DEFINITIONS OF ARITHMETICAL SIGHTS 

EMPLOYED IN THE FOLLOWING CALCULATIONS, "WH1CB 
0U6HT TO BE PARTICULARLY ATTENDED TOy 











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25 




^ J -^_ Dt_ ^5i, 


DECIMAL 


APPROXIMATIONS, 


fcOR FACILITATING CALCULATIONS IN MENSURATION* 


Lineal feet multiplied by -00019 


= miles* 




" yards 


" 


•000568 


— " 




Square inches 


(( 


•007 


ca square 


feet. 


u yards 


(< 


•000206/ 


as acres. 




Gircular inches 


(( 


•00546 


== square 


feet. 


Cylindrical inches 


(( 


•0004546 


= cubic feet. 


11 feet 


<( 


•02909 


— cubic y 


ards. 


Cubic inches 


II 


•00058 


£± cubic feet. 


" feet 


«( 


•03704 


— cubic yards. 


t< « 


II 


6-232 


— imperial gallons* 


" inches, 


(< 


•003607 


£= " 


14 


Cylindrical feet 


" 


4-895 


= «« 


it 


" inches 


II 


•002832 


s-s " 


ii 


Cubic inches 


(I 


•263 


= lbs. ars. of cast iron* 


n 11 


" 


•281 


as " 


wrought iron. 


ti u 


II 


•283 


.— . «« 


steeh 


it <« 


is 


•3225 


ss " 


copper. 


u << 


II 


•3037 


= " 


brass. 


t< t« 


<l 


•26 


s= " 


zinc. 


<{ (< 


II 


•4103 


B " 


lead. 


«( (< 


II 


•2636 


SS " 


tin. 


it « 


II 


•4908 


= " 


mercury. 


Cylindrical inches 


II 


•2065 


—? II 


cast iron. 


" 


It 


•2168 


— _ II 


wrought iron* 


t( 


II 


•2223 


== " 


steel. 


<« 


II 


•2533 


— II 


copper. 


«« 


II 


•2385 


=5 " 


brass. 


« 


II 


•2042 


=± " 


zinc. 


it 


II 


•3223 


_ II 


lead. 


II 


" 


•207 


a « 


tin. 


II 


II 


•3854 


— ii 


mercury. 


Avoirdupois lbs. 


II 


•009 


= cwts. 




i< 


(4 


•00045 


= tons. 


J..-.:..--: : — I 



26 



DECIMAL EQUIVALENTS. 



DECIMAL EQUIVALENTS TO FRACTIONAL 
PARTS OF LINEAL MEASURES. 



One inch, the integer, or whole number. 


•96875 i & ^ 
'9375 7 & J ¥ 
•90625 I&^ 
'875 g 1 


•625 4 
•59379 | & ^ 
•5625 | &T 1_ 
'53125 o|&^ 


•28125 | & A 

•21875 i&A 
•1875 o i& J_ 


•84375 | | & 8 
•8125 £ |& ^ 

•78125 | }*A 
•75 * 3 

'71875 5 3 

8 3T 
•6875 | & 1 

•65625 | &A 


' 5 1 1 

'46875 g. ^ &A 

•4375 g 1 & J- 
•40625 * { & X 
•375 3 
•34375 | &A 
•3125 | &T 1_ 


" 15625 1 i&*V 

•125 g. | 
•09375 g 8 
•0625 * V 
'03125 jj 




One fo 


at, or 12 inches, the integer. 


•9166 11 inches, 


'4166 fi inches. 


•0625 8 of inch. 
•0628 £ 6. « 
•04166 "g I « 
•03125 » 8 '« 
'02083 | 1 " 

•01041 I " 

¥ 


•6333 £ 10 " 

•75 § 9 « 


•3333 * 4 " 
•25 1 3 " 


•6666 » 8 « 


•1666 ©2 " 


•5833 | 7 « 


•0833 | 1 " 


•5 6 «« 


•07291 1 " 
8 


One ya 


rd, or 36 inches, the 


Integer. 


•9722 35 inches. 


•6389 23 inches. 


•3055 11 inches. 


•9445 34 " 


•6111 22 « 


•2778 10 « 


•9167 33 " 


•5833 21 « 


•25 9 " 


•8889 32 " 


•5556 20 " 


•2222 8 " 


'8611 ^ 31 " 
'8333 H 30 «« 


•5278 £ 19 '« 
•5 ? 18 " 


•1944 £ 7 u 
•1666 ? 6 •« 


•8056 « 29 " 
•7778 § 28 " 


•4722 Sf 17 « 
•4445 | 16 " 


•1389 » 5 " 
•1111 | 4 " 


•75 27 " 


•4166 15 " 


•0833 3 " 


•7222 26 « 


•3889 14 « 


•555 2 " 


•6944 25 " 


•3611 13 " 


•0277 1 " 


•6667 24 " 


•3333 12 « 





27 



MENSURATION. 

Mensuration is that branch of Mathematics which 
is employed in ascertaining the extension, solidities, 
and capacities of bodies, capable of being measured. 

1. MENSURATION OF SURFACE. 

To measure or ascertain the quantity of surface in 
any right-lined figure whose opposite sides are parallel 
to each other, as a 

Square, Rectangle, Rhomboid, 



&c. 



Rule. — Multiply the length by the breadth; the 
product is the area or superficial contents. 

Application of the Bute to practical Purposes. 

1. The side of a square piece of board is 8 T 3 ^ inches 
in length ; required the area or superficies. 

Decimal equivalent to the fraction -^. = -1875, (see page 26 ;) 
and 8-1875 X 8-1875 = 67*03515625 square inches, the area. 

2. The length of the fire grate under the boiler of a 
steam engine is 4 feet 7 inches, and its width 3 feet 

6 inches ; required the area of the fire grate. 

7 in. = -5833 and 6 in. = -5, (see Table of Equivalents, p. 26 ;.) 

hence 4-5833 x 3-5 = 16-04155 square feet, the area. 

3. Required the number of square yards in a floor 
whose length is 13-|, and breadth 9| feet. 

13-5 X 9-75 = 131-625-^-9= 14-625 square yards. 

Note 1. — The above rule is rendered equally applicable 
to figures whose sides are not parallel to each other, by 
3* 



28 MENSURATION. 

taking the mean breadth as that by which the contents 
are to be estimated. 

2. The square root of any given sum equals the side of a 
square of equal area. 

3. Any square whose side is equal to the diagonal of 
another square, contains double the area of that square. 

4. Any sum or area, (of which to form a rectangle,) 
divided by the breadth, the quotient equals the length ; or 
divided by the length, the quotient equals the breadth of 
the rectangle required. 

TRIANGLES. 

Any two sides of a right-angled triangle being given, 
to find the third side. 

Bute 1. — Add together the squares of the base and 
perpendicular, and the square root of the sum is the 
hypotenuse or longest side. 

Rule 2. — Add together the hypotenuse and any one 
side, multiply the sum by their difference, and the 
square root of the product equals the other side. 

Application to practical Purposes. 

1. Wanting to prop a building with raking shores, 
the top ends of which to be 25 feet from the ground, 
and the bottom ends 16 feet from the base of the build- 
ing; what must be their length, independent of any ex- 
tra length allowed below the surface of the ground ? 

25 2 + 16 2 = V 881 = 29-6816 feet, or -6816 X 12 = 8 inches ; 
consequently, 29 feet 8 inches nearly. 

2. From the top of a wall 18 feet in height, a line 
was stretched across a canal for the purpose of ascer- 
taining its breadth ; the length of the line, when meas- 
ured, was found to be 40 feet ; required the breadth 
from the opposite embankment to the base of the wall. 

40 — 18 = 22, and 40+ 18 X 22 = vl276 = 3572, or 35 feet 
9 inches nearly, the width of the canal. 

Triangles similar to each other are proportional to 
each other ; hence their utility in ascertaining the 
heights and distances of inaccessible objects. 



MENSURATION. 



29 



A.^- 



-1 



Thus, suppose the height 
of an inaccessible object D is 
required ; I find by means of 
two staffs, or otherwise, the 
height of the perpendicular 
B C and the length of the 
base line A B ; also the dis- 
tance from A to the base of the objeet G D ; 

then AB:BC::AG:GD. And suppose A B = 6 feet, 

BC=2 feet, and A G = 150 

-6 : 2 — 150 : 50 feet, the height of D from G. 

. A 

Again, -suppose the inaccessible dis- 
tance A be required ; mahe the line B A, / 
B C, a right angle, and B C of three or / 
four equal parts of any convenient -dis- /' 
tance, through one of which, and in a ^ / T 
line with the object A, determine the 
triangle CDF.; then the proportion will 
be as 



C F : C D : : B F : B A. Let C F = 10 yards, C D = 53, and 
B F = 30, 10: 53 : : 30 : 159 yards, the distance from B. 

To Jind the area of a triangle when the base and 
perpendicular are given. 

Rule. — Multiply the base by the perpendicular 
height, and half the product is the area. 

L The base of the tri- 
angle A D B is 11^ inches 
in length, and the height D 
<C, 3J- inches ; required the 




•00375 and |.= -375, (see p. 26 :) 



fee nee 



11-09375 X 3-375 
% 



= 18-72075 square inches, the area. 



30 MENSURATION. 

2. The base of a triangle is 53 feet 3 inches, and 
the perpendicular 7 feet 9 inches ; required the area 
or superficies. 

5 3-25 x 7;75 _ 2 06-34375 square feet, the area. 

When only the three sides of a triangle can be given y 
to find the area. 

Rule. — From half the sum of the three sides sub- 
tract each side severally j multiply the half sum and 
the three remainders together, and the square root 
of the product is equal the area required. 

Required the area of a triangle, whose three sides 
are respectively 50, 40, and 30 feet. 

— ■ — = 60, or half the sum of the three sides. 

60 — 30 = 30 first difference, 
60 — 40 = 20 second difference, 
60 — 50 = 10 third difference, 
then 30 X 20 X 10 x 60 = V360000 = 600, the area required. 

Triangles are employed to >^\~~~^~~~---~---w 

great advantage in deter- jS \ \ /f\^v^ 

mining the area of any recti- <*~ \ \ /' / \J^\ 

lineal figure, as the annexed, \. \ \ / X l 

and by which the measure- ^y u__ — "^i\/ 

ment is rendered compara- nL^^^ 
tively simple. 



POLYGONS. 

Polygons, being composed of triangles, may of 
course be similarly measured ; hence, in regular poly* 
gons, multiply the length of a side by the perpendicular 
height to the centre, and by the number of sides, and 
half the product is the area. 



MENSURATION* 



31 



I 





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« 



OZ MENSURATION. 

Application of the Table. 

1. The radius of a circle being 6£ feet, required 
the side of the greatest heptagon that may be in- 
scribed therein. 

•867 X 6'5 s= 5-6355, or 5 feet 7A inches nearly. 

2. Each side of a pentagon is required to be 9 feet \ 
required the radius of circumscribing circle. 

•852 X9= 7-668, or 7 feet 8 inches. 

3. A perpendicular from the centre to either side 
of an octagon is required to be 12 feet ; what must 
be the radius of circumscribing circle ? 

1-08 X 12 = 12-96, or 12 feet 11£ inches. 

4. Each side of a hexagon is 4£ yards ; required 
its superficial contents. 

4J^ X 2-598 = 52*6095 square yards. 

THE CIRCLE AND ITS SECTIONS. 

Observations and Definitions. 

1. The circle contains a greater area than any other 
plane figure bounded by the same perimeter or outline. 

2. The areas of circles are to each other as the 
squares of their diameters ; any circle twice the diam- 
eter of another contains four times the area of the 
other. 

3. The radius of a circle is a 
straight line drawn from the centre 
to the circumference, as O B. 

4. The diameter of a circle is a 
straight line drawn through the 
centre, and terminated both ways 
at the circumference, as CO A, 

5. A chord is a straight line joining any two poirrt9 
of the circumference, as D F. 

6. The versed sine is a straight line joining the 
chord and circumference, as E G. 




MENSURATION. 3d 

7. An arc is any part of the circumference, as C D E. 

8. A semicircle is half the circumference cut off by 
a diameter, as C E A. 

9. A segment is any portion of a circle cut off by a 
chord, as D E F. 

10. A sector is a part of a circle cut off by two 
radii, as A O B. 

General Rules in Relation to the Circle. 

1. Multiply the diameter by 3*1416, the product is 
the circumference. 

2. Multiply the circumference by '31831, the product 
is the diameter. 

3. Multiply the square of the diameter by '7854, 
the product is the area. 

4. Multiply the square root of the area by 1-12837, 
the product is the diameter. 

5. Multiply the diameter by -8862, the product is 
the side of a square of equal area. 

6. Multiply the side of a square by 1*128, the 
product is the diameter of a circle of equal area. 

Application of the Rules as to Purposes of Practice. 

1. The diameter of a circle being 7 T 8 ¥ inches, re- 
quired its circumference. 

7*1875 X 3*1416 •= 22*58025 inches, the circumference. 
Or, the diameter being 30-£ feet, required the cir- 
cumference. 

3-1416 X 30*5 = 95*8188 feet, the circumference. 

2. A straight line, or the circumference of a circle, 
being 274*89 inches, required the circle's diameter 
corresponding thereto. 

274*89 X *31831 = 87*5 inches diameter. 
Or, what is the diameter of a circle, when the cir- 
cumference is 39 feet ? 

31831 X 39 = 12-41409 feet, and -41409 X 12 = 4*96908 inches, 
or 12 feet 5 inches, very nearly the diameter. 



34 MENSURATION. 

8. The diameter of a circle is 3| inches ; what is its 
area in square inches ? 

3-75 2 = 14-0625 X '7854 as 11-044, &c„ inches area. 
Or, suppose the diameter of a circle 25 feet G 
inches, required the area. 

25-5 2 = 650-25 X -7854 = 510-706, &c, feet, the area. 

4. What must the diameter of a circle be, to con- 
tain an area equal to 706-86 square inches ? 

^7~0lT8ef= 26-586 x 1-12837 = 29-998 or 30 inches, the diam- 
eter required. 

5. The diameter of a circle is 14^ inches ; what 
must I make each side of a square, to he equal in area 
to the given circle ? 

14-25 X '8862 = 12-62835 inches, length of side required. 

Any chord and versed sine of a circle being given, 
to find the diameter. 

Bute. — Divide the sum of the 
squares of the chord and versed sine 
by the versed sine, the quotient is 
the diameter of corresponding circle. 

1. The chord of a circle A B 
equal 6-| feet, and the versed sine 
C D equal 2 feet, required the cir- 
cle's diameter. 



6-5 2 + 2 2 = 46-25 -i- 2 = 23-125 feet, the diameter. 

2. In a curve of a railway, I stretched a line 72 feet 
in length, and the distance from the line to the curve 
I found to be 1^ ft.; required the radius of the curve. 

72 2 +lW=5185-5625, and 5 1 1 ^' 56 ^°=2074-225 ft., the radius. 
l'Zo X & 

To find the length of any given arc of a circle. 

&ule. — From eight times the chord of half the arc 
subtract the chord of the whole arc, and one third of 
the remainder is equal the length of the arc. 



MENSURATION. 



35 




Required the length 
of the arc ABC, the 
chord A B of half the 
arc being 4 feet 3 inches, 
and chord A C of the whole arc 8 feet 4 inches. 

4-25 X 8 = 34, and 34 — 8-333 =^~ 7 - = 8-555 feet, ' 

the length of the arc. 

To find the area of the sector of a circle. 
Rule. — Multiply the length of the arc by its radius, 
and half the product is the area. 

The length of the arc A C B, 
equal 9^ feet, and the radii F A, 
F B, equal each 7 feet, required the 
area. 

9-5x7 = 65-5 -^ 2 = 32-75, the area. 

Note. — The most simple means 
whereby to find the area of the segment 
of a circle is, to first find the area of a 
sector whose arc is equal to that of the 
given segment ; and if it be less than a semicircle, subtract 
the area of the triangle formed by the chord of the segment 
and radii of its extremities ; but if more than a semicircle, 
add the area of the triangle to the area of the sector, and the 
remainder, or sum, is the area of the segment. 

Thus, suppose the area of the segment A C B e is required, 
and that the length of the arc A C B equal 9| feet, F A and 
F B each equal 7 feet, and the chord A B equal 8 feet 4 
inches, also the perpendicular e F equal 3| feet. 
9-75 X 7 




= 34-125 feet, the area of the sector. 



8-333 X 3-75 



15-624 feet, the area of the triangle. 



And 34-125 — 15-624 = 18-501 feet, the area of the segment. 

To find the area of the space contained between two 
concentric circles. 

Rule. — Multiply the sum of the inside and outside 
diameters by their difference, and by -7854, the product 
is the area. 

4 



86 MENSURATION. 

1. Suppose the external circle 
A B equal 32 inches, and internal 
circle C D equal 28 inches ; re- 
quired the area of the space con- 
tained between them. 




32 + 28 - 60, and 32 — 28 - 4, hence 
60 X 4 X -7854 = 188-496 in., the area. 

2. The exterior diameter of the fly-wheel of a steam 
engine is 20 feet, and the interior diameter 18^ feet ; 
required the area of the surface or rim of the wheel. 



20 -+- 18-5 - 38-5 and 20 — 18-5 = 1-5, hence 38-5 X 1-5 X '7854 
= 45 - 35j &c, feet, the area. 

To find the area of an ellipsis or oval. 

Ride. — Multiply the longest diam eter by the shortest, 
and the product by •7854 ; the result is the area. 

An oval is 25 inches by 16*5 ; what are its superfi- 
cial contents ? 

25 X 16-5=412-5 x '7854 = 323-9775 inches, the area. 

Note. — Multiply half the sum of the two diameters by 
3-1416, and the product is the circumference of the oval or 
ellipsis. 

To find the area of a parabola, or its segment. 

Rule. — Multiply the base by the perpendicular 
height, and two thirds of the product is the area. 

What is the area of a parabola whose base is 20 feet 
and height 12 ? 

20 x 12 = 240 3 X2 = 160 feet, the area. 

Note. — Although the whole of the preceding practical 
applications or examples are given in measures of feet or 
inches, these being considered as the most generally familiar, 
yet the rules are equally applicable to any other unit of 
measurement whatever, as yards, chains, acres, &c, &c, 8r* 



MENSURATION. 37 



2. MENSURATION OP THE SUPERFICIES, SOLID- 
ITIES, AND CAPACITIES OP BODIES. 

To find the solidity or capacity of any figure in the 
cubical form. 

Bute. — Multiply the length of any one side by its 
breadth and by the depth or distance to its opposite 
side ; the product is the solidity or capacity, in equal 
terms of measurement. 

Application of the Rule to practical Purposes. 

1. Required the number of cubic inches in a piece 
of timber 23-| inches long, 7f inches broad, and 3-| 
inches in thickness. 

23-5 X 775 x 3-625 = 660-203 cubic inches. 

2. A rectangular cistern is in length 8-^- feet, in 
breadth o\ feet, and in depth 4 feet ; required its ca- 
pacity in cubic feet, also its capacity in British impe- 
rial gallons. 

8-5 X 525 X 4 = 178-5 cubic feet, and 178-5 X 6-232 ( see Table 
of Decimal Approximations, p. 25) = 1112*412 gallons. 

3. A rectangular cistern, capable of containing 520 
imperial gallons, is to be 7-^ feet in length, and 4-£ feet 
in width ; it is required to ascertain the necessary 
depth. 

7-25 X 4-5 X 6-232 = 203-318, and f°'!!! = 2 ' 55 7 feet, or 2 

feet 6| inches, nearly. 

4. A rectangular piece of cast iron, 20 inches long 
and 6 inches broad, is to be formed of sufficient 
dimensions to weigh 150 lbs. ; what will be the depth 
required ? 

20 X 6 X -263 (see Table of Decimal Approximations, Cast 
Iron, p. 25) = 31-96, and gy.gg = 4-69 in., or 4 and 11 in., 
the thickness required. 



38 MENSURATION. 

To find the convex surface, and solidity or capacity f 
of a cylinder, 

Rule 1. — Multiply the circumference of the cylin- 
der by its length or height ; the product is the convex 
surface. 

Rule 2. — Multiply the area of the diameter by the 
length or height, and the product is the cylinder's 
solidity or capacity, as may be required. 

Application of the Rules, 

1. The circumference of a cylinder is 37^- inches, 
and its length 54| inches ; required the convex surface 
in square feet. 

5475 X 37'5 X '007 (see Table of Approximations) = 14-371 
square feet. 

2. A cylindrical piece of timber is 9 inches diame- 
ter, and 3 feet 4 inches in length ; required its solidity 
in cubic inches, and also in cubic feet. 

3 feet 4 inches & 40 inches, and 9 9 X 7854 X 40 = 2544-696 
cubic inches ; then 2544-696 X . 00058 m 1-4759 cubic feet. 

3. Suppose a well to be 4 feet 9 inches diameter, and 
16^ feet from the bottom to the surface of the water ; 
how many imperial gallons are therein contained? 

475 2 x 16-5 x 4-895 = 1822-162 gallons. 

4. Again, suppose the well's diameter the same, and 
its entire depth 35 feet ; required the quantity in cubic 
yards of material excavated in its formation. 

4-75 2 X 35 X -02909 = 22-973 cubic yards. 

5. I have a cylindrical cistern capable of holding 
7068 gallons, and its depth is 10 feet ; now I want to 
replace it with one of an equal depth, but capable of 
holding 12,500 gallons ; what must be its diameter? 

4-895 X 10 = 48-95, and ^|^° = */?WZ = 15-9687 feet, or 
15 feet llf inches. 

6. A cylindrical piece of lead is required, 1\ inches 



MENSURATION. 



39 



diameter, and 168 lbs. in weight; what must be its 
length in inches ? 

7-52 x -3223 



18, and -^ - 9-3 inches. 



To find the length of a cylindrical helix, or spiral, 
wound round a cylinder. 

Rule. — Multiply the circumference of the base by 
the number of revolutions of the spiral, and to the 
square of the product add the square of the height ; 
the square root of the sum is the length of the spiral. 

Application of the Rule. 

1. Required the length of the thread or screw twist- 
ing round a cylinder 22 inches in circumference 3^ 
times, and extending along the axis 16 inches. 

22 x 3-5 = 77 2 = 5929, and 16 2 = 256, then V5929 + 256 
= 78-64 inches. 

2. The well of a winding staircase is 5 feet diameter, 
and height to the top landing 25 feet ; the hand-rail is 
to make 2\ revolutions ; required its length. 

5 feet diameter = 15*7 feet circumference. 
15-7 X 2-5 = 39-2 5 2 = 1540-5625, and 25 2 = 625, then 
a/154'J -f- 625 = 46-5 feet, the length required. 
To find the convex surface, solidity, or capacity of 
a cone or pyramid. 

Rule 1 . — Multiply the circumference of the base by the 
slant height, and half the product is the slant surface. 
Rule 2. — Multiply the area of the base by the per- 
pendicular height, and one third of the product is the 
solidity or capacity, as may be required. 

Application of the Rules. 
1. Required the area, in square inches, of the slant 
surface of a cone whose slant height equal 18| inches, 



and diameter at the base 6^ inches. 

6-25 X 3-1416 = 19-635 circumference of the base 
19-635x18-75 10 . n _ 01Q . . , 
~ = 184-078125 square inches. 



and 



40 MENSURATION. 

2. Required the quantity of lead, in square feet 
sufficient to cover the slant surface of a hexagonal pyr- 
amid whose slant height is 42 feet, and the breadth 
of each side at the base 4 feet 9 inches. 

4-75 X 42 x 6 sides e 
= 598*5 square feet. 

3. What is the solidity of a cone, in cubic inches, 
the diameter at the base being 15 inches, and per- 
pendicular height 32-| inches ? 

15 2 X -7854x32-5 1Q1 . ._._ ,. . . 

- = 1914-4125 cubic inches. 

o 

4. In a square solid pyramid of stone 67 feet in 
height, and 16^ feet at the base, how many cubic feet? 

16-5x16-5x67 cnQAO s u- c * 
- = 6080-25 cubic feet. 

o 

To find the solidity or capacity of any frustum of a 
cone or pyramid. 

Rule. — If the base be a circle, add into one sum the 
two diameters, or, if a regular polygon, the breadth 
of one side at the top and at the base ; then from the 
square of the sum subtract the product of these di- 
ameters or breadths ; multiply the remainder by -7854, 
if a circle, or by the tabular area (see Table of Poly- 
gons, p. 31) and by one third of the height; and the 
product is the content in equal terms of unity. 

Note. — Where the whole height of the cone or pyramid can 
be obtained, of which the given frustum forms a part, the most 
simple method is, first to find the whole contents, then the 
contents extending beyond the frustum ; 
and, subtracting the less from the greater, 
leaves the contents of the frustum required. 

Application of the Rides. 
1. The perpendicular height A B 
of the frustum of a hexagonal pyra- 
mid C D E, is 7-| feet, and the breadth 
of each side at top and base equal 
3f and 2-| feet ; required the solid 
contents of the frustum in cubic 
feet. 




MENSURATION. 



41 




3-75 + 2-5 = 6-25, and 6-25 X 6-25 = 39-0625, then 3-75x2-5 = 
9-375, and 39-0625— 9-375 = 29-6875x2-598 (tabular area, p. 
31) = 77-138 X 25 or £ of the height = 192-845 cubic feet. 

2. Required the solidity of the frustum of a cone, 
the top diameter of which is 7 inches, the base diame- 
ter 9-^, and the perpendicular height 12. 

7 4-9-5 a = 272-25, and 7x9-5 = 66-5, then 272-25—66-5 = 
205-75 X -7854 = 161-576 X 4 or £ of the height = 646-3 
cubic inches. 

3. A vessel in the form of an in- 
verted cone, as A B C D, is 5 feet in 
diameter at the top, 4 feet at the 
bottom, and 6 feet in depth ; re- 
quired its capacity in imperial gal- 
lons. 

5 + 4 = 9 2 = 81, and 5 X 4 = 20, hence 81 — 20 = 61 X '7854, 
and by 2 or £ of the depth = 95*8188 cubic feet, and X 6-232 
= 597-1427 gallons. 

To find the solid contents of a wedge. 

Rule. — To twice the length of the base add the 
length of the edge ; multiply the sum by the breadth 
of the base, and by the perpendicular height from the 
base, and one sixth of the product is the solid contents. 

Application of the Rule. 

Required the solidity of a wedge, in 

cubic inches, the base ABCD being 9 

inches by 3£, the edge E F 7 inches, 

and the perpendicular height G E 15. 



= 218-75 cubic inches. 




18- + 7 X 3-5 X 15 

6 

To find the convex surface, the solidity, or the 
capacity of a sphere or globe. 

Rule I. — Multiply the square of the diameter by 
3*1416 ; the product is the. convex surface. 

Rule 2. — Multiply the cube of the diameter by 
5236 ; the product is the solid contents. 



42 MENSURATION. 

Rule 3. — Multiply the cube of the diameter in feet 
by 3*263, or in inches by -001888 ; the product is the 
capacity in imperial gallons. 

Application of the Rules. 

1. Required the convex surface, the solidity, and 
the weight in cast iron of a sphere or ball 10£ inches 
in diameter. 

10-5 2 X 3-1416 = 346-3614 square inches. 
10-5 3 X -5236 = 606-132, &c, cubic inches ; and 
606-132 x -263 (see Table of Approximations, p. 25) = 
159-4 lbs. 

2. A hollow or concave copper ball is required, 8 
inches diameter, and in weight just sufficient to sink to 
its centre in common water ; what is the proper thick- 
ness of copper of which it must be made ? 

Weight of a cubic inch of water = -03617 lbs. ) „ co 

copper = -3225 " \ see P' 63 * 

8 3 X -5236 X -03617 A QAQOQ . . , t . ,. , 
~ = 4*84828 cub. m. of water to be displaced. 

4*84828 
And 0OO = 15-0334 cubic inches of copper in the ball. 
'oZZo 

Then 8 2 X 3-1416 = 201-0624, and l5 '-^ 3 ^- = -0747 inches, the 

201-0624 ' 

thickness of copper required. 

•0747 X 16 = T !g. of an inch full, or 3 lbs. copper to a square 
foot. 

3. What diameter must I make a leaden ball, so as 
to weigh 72 lbs. ? 

•5236 X -4103 = -21483308, and . 214 q| 3Q8 = V340 = 6-97 
inches, diameter. 



INSTRUMENTAL ARITHMETIC, 



UTILITY OF THE SLIDE RULE* 



The slide rule is an instrument by which the greater 
portion of operations in arithmetic and mensuration 
may be advantageously performed, provided the lines 
of division and gauge points be made properly correct, 
and their several values familiarly understood. 

The lines of division are distinguished by the letters 
A B C D ; A B and C being each divided alike, and 
containing what is termed a double radius, or double 
series of logarithmic numbers, each series being sup- 
posed to be divided into 1000 equal parts, and dastrib* 
Uted along the radius in the following manner : — 

om 1 to 2 contains 301 of those parts, being the log. of 2, 



477 
602 
699 
778 
845 
903 
954 



1000 being the whole-number* 

The line D, on the improved rules, consists of only 
a single radius 5 and although of larger radius, the 
logarithmic series is the same, and disposed of along 
the line in a similar proportion, forming exactly a line 
of square roots to the numbers on the lines B C» 



44 INSTRUMENTAL ARITHMETIC. 



NUMERATION. 

Numeration teaches us to estimate or properly value 
the numbers and divisions on the rule in an arithmet- 
ical form. 

Their values are all entirely governed by the value 
set upon the first figure, and, being decimally reckoned, 
advance tenfold from the commencement to the termi- 
nation of each radius : thus, suppose 1 at the joint be 
one, the 1 in the middle of the rule is ten, and 1 at the 
end one hundred : again, suppose 1 at the joint ten, 1 
in the middle is 100, and 1 or 10 at the end is 1000, 
&c, the intermediate divisions on which complete the 
whole system of its notation. 



TO MULTIPLY NUMBERS BY THE RULE. 

Set 1 on B opposite to the multiplier on A ; and 
against the number to be multiplied on B is the prod- 
uct on A. 

Multiply 6 by 4. 

Set 1 on B to 4 on A; and against 6 on B is 24 on A. 
The slide thus set, against 7 on B is 28 on A. 



8 


<< 


32 " 


9 


(< 


36 " 


10 


" 


40 " 


12 


« 


48 " 


15 


« 


60 " 


25 


H 


100, &c. &<5 



TO DIVIDE NUMBERS UPON THE TtULE. 

Set the divisor on B to 1 on A ; and against the 
number to be divided on B is the quotient on A. 
Divide 63 by 3. 

Set 3 on B to 1 on A ; and against 63 on B is 21 on A. 



_*_ — , — - . i , 



INSTRUMENTAL ARITHMETIC, 



45 



PROPORTION, OR RULE OF THREE DIRECT. 

Rule. — Set the first term on B to the second on A ; 
find against the third upon B is the fourth upon A. 

1. If 4 yards of cloth Cost 38 shillings, what will 30 
yards cost at the same rate ? 

Set 4 on B to 38 on A ; and against 30 on B is 285 shil- 
lings on A. 

2. Suppose I pay 31s. 6d. for 3 ewt. of iron; at what 
rate is that per ton ? 1 ton ss 20 cwt. 

Set 3 upon B to 31-5 upon A ; and against 20 upon B is 
210 upon A. 



RULE OF THREE INVERSE, 

Bute. — Invert the slide, and the operation is the 
same as direct proportion. 

1. I know that six men are capable of performing a 
certain given portion of work in eight days, but I want 
the same performed in three ; how many men must 
there be employed ? 

Set 6 upon C to 8 upon A ; and against 3 upon C is 16 
upon A. 

2. The lever of a safety valve is 20 inches in length, 
and 5 inches between the fixed end and centre of the 
valve ; what weight must there be placed on the end 
of the lever to equipoise a force or pressure of 40 lbs. 
tending to raise the valve ? 

Set 5 upon C to 40 upon A ; and against 20 on C is 10 
on A. 

3. If 8f yards of cloth, \\ yards in width, be a 
sufficient quantity, how much will be required of 
that which is only -|ths in width, to effect the same 
purpose ? 

Set 1*5 on C to 8 - 75 on A ; and against "875 upon C is 15 
yards upon A. 



48 



INSTRUMENTAL ARITHMETIC. 



upon C is 30 



SQUARE AND CUBE ROOTS OF NUMBERS. 

On the engineer's rule, when the lines C and D are 
equal at both ends, C is a table of squares, and D a 
table of roots, as — 

Squares-, 1 4 9 16 25 36 49 64 81 on C. 
Roots, 123 4 5 6 7 8 9 on D. 

Tojlnd the geometrical mean proportion between 
two numbers* 

Set one of the numbers upon C to the same number 
upon D 5 and against the other number upon C is the 
mean number or side of an equal square upon D. 

Required the mean proportion between 20 and 45. 

Set 20 upon C to 20 upon D ; and against 45 
onD. 

To cube any number, set the number upon C to 1 
or 10 upon D ; and against the same number upon D 
is the cube number upon C. 

Required the cube of 4. 

Set 4 upon C to 1 or 10 upon T> ; and against 4 upon D is 
64 upon C. 

To extract the cube root of any number, invert the 
slide, and set the number upon B to 1 or 10 upon D ; 
and where two numbers of equal value coincide, on 
the lines B D, is the root of the given number. 

Required the cube root of 64. 

Set 64 upon B to 1 or 10 upon D ; and against 4 upon B 
is 4 upon D, or root of the given number. 

On the common rule, when 1 in the middle of the 
line C is set opposite to 10 on D, then C is a table of 
squares, and "D a table of roots. 

To cube any number by this rule, set the number 
upon C to 10 upon D ; and against the same number 
upon D is the cube upon C. 



INSTRUMENTAL MENSURATION. 47 



MENSURATION OF SURFACE* 

1. Squares, Rectangles, &c. 

Rule. — When the length is given in feet and the 
breadth in inches, set the breadth on B to 12 on A ; 
and against the length on A is the content in square 
feet on B. 

If the dimensions are all inches, set the breadth on 
B to 144 upon A ; and against the length upon A is 
the number of square feet on B. 

Required the content of a board 15 inches broad 
and 14 feet long. 

Set 15 upon B to 12 upon A ; and against 14 upon A is 
17*5 square feet on B. 

2. Circles, Polygons, &c. 
Rule. — Set -7854 upon C to 1 or 10 upon D ; then 
will the lines C and D be a table of areas and diameters. 

Areas, 3-14 7.06 12-56 19-63 28*27 38-48 50-26 63-61 upon C. 
Diam.,2 „S456739 uponD. 

In the common rule, set -7854 on C to 10 on D ; 
then C is a line or table of areas, and D of diameters, 
as before. 

Set 7 upon B to 22 upon A ; then B and A form or 
become a table of diameters and circumferences of 
circles. 

Cir., 3-14 6-28 9-42 12-56 15-7 18-85 22 25-13 28-27 upon A. 
Dia.,1 234 56 789 upon B. 

Polygons from 3 to 12 sides. — Set the gauge-point 
upon C to 1 or 10 upon D ; and against the length of 
one side upon D is the area upon C. 
Sides, 3 5 6 7 8 9 10 11 12. 

Gauge-points, -433 1-7 2-6 3-63 4-82 6-18 7*69 9-37 11-17 

Required the area of an equilateral triangle, each 
side 12 inches in length. 

Set -433 upon C to 1 upon D ; and against 12 upon D are 
62-5 square inches upon C. 
5 



f, L - •"- ' — - • — — — - 










iS JtfSTKTJMENTAL MENSURATION. 








; : 

! 


TABLE OF GAUGE-POINTS FOR THE ENGINEER'S RULE. 




Names'. 


F,F,F. 


F,l,l. 

83 


li I, i* 

1728 


F.I. 

106 


I,i. 


F. 


i. 

121 


Cubic inches,, 


578 


1273 


105 


: 


Cubic feet r 


1 


144 


1 


1833 


22 


121 


33 






Imp* gallons 


163 


231 


277 


294 


353 


306 


529 






j Water in lbs. 


16 


23 


276 


293 


352 


305 


528 






\ Gold- 


814 


1175 


141 


149 


178 


155 


269 






Silver " 


15 


216 


261 


276 


334 


286 


5 




. 


Mercury ** 


118 


169 


203 


216 


258 


225 


389 






Brass M 


193 


177 


333 


354 


424 


369 


637 




Copper ** 


18- 


26 


319 


331 


397 


345 


596 






Lead ** 


141 


203 


243 


258 


31 


27 


465 






Wro'tiron" 


207 


297 


357 


338 


453 


394 


682 






Cast iron ** 


222 


32 


384 


407 


489 


424 


733 




| 


Tin 


219 


315 


378 


401 


481 


419 


728 




: 


Steel H 


202 


292 


352 


372 


448- 


385 


671 






Coal 


127 


183' 


22 


33 


28 


242 


42 






t Marble " 


591 


85 


102 


116 


13 


113 


195 




• 


' Freestone " 


632 


915 


11 


11*2 


14 


141 


21 




| 

1 


FOR THE COMMON SLIDE 


RULE. 




^ 




Names. 


F,F,F. 

36 


F. 1. 1. 

518 


I, i, I. 

624 


F.I. 

660 


1,1. 

799 


F. 


I. 

113 


Cubic inches, 


625 




Cubic feety 


625 


9 


108 


114 


133 


119 


206 






Water ,in lbs. 


10 


144 


174 


184 


22 


191 


329 






Gold 


507 


735 


88 


96 


118 


939 


180 






Silver " 


938 


136 


157 


173 


208 


173 


354 




! 


Mercury " 


738 


122 


127 


132 


162 


141 


242 




, t 


Brass M 


12 


174 


207 


221 


265 


23 


397 






Copper '• 
Lead 


112 


163 


196 


207 


247 


214 


371 




s 


880 


126 


152 


162 


194 


169 


289 






Wro'tiron" 


129 


186 


222 


235 


283 


247 


423 






Cast iron " 


139 


2 


241 


254 


304 


265 


458 




! 


Tin " 


137 


135 


235 


25 


300 


261 


454 






Steel 


136 


183 


22 


233 


278 


239 


418 






Coal " 


795 


114 


138 


146 


176 


151 


262 






Marble " 


370 


53 


637 


725 


81 


72 


121 




■ 


Freestone " 


394 


57 


69 


728 


873 


755 


132 




•■■«" — 


- — n(. .,.,. .„ — a — ^u- 








. ,.,. , 


. . 


":■;- &e 


. • 


■-- v.-.-,.,.- 



INSTRUMENTAL MENSUBATtONi 



49 



Mensuration of solidity and capacity. 

General rule. — Set the iength Upon B to the gauge* 
point Upon A j and against the side of the square, of 
diameter on D, are the cubic contents^ or weight in 
lbs. on d 

1. Required the cubic contents of a tree 30 feet in 
length, and 10 inches quarter girt. 

Set 20 Upon B to 144 (the gauge-point) Upin A 5 and 
against 10 upon D is 20*75 feet upon C* 

% In a cylinder 9 inches in length and 1 inches 
diameter, how many cubic inches ? 

Set 9 upon B to. 1273 (the gaUge-^polnt) Upon A; and 
against 7 on D is 846 inches ori d 

3. What is the weight of a bar of cast iron 3 inches 
square, and 6 feet long ? 

Set 6 upon B to 32 (the gauge-point) upon A 5 and 
against 3 upon D is 168 lbs* upon C» 

By the common ruld 

4* Required the weight of a cylinder of wrought iron 
iO inches longj and 5\ diameter* 

Set 10 upon B to 283 (G. Pt.) upon A \ and against 5£ 
upon D is 66-65 lbs. on 0. 

5* What is the weight of a dry rope 25 yards long, 
and 4 inches circumference ? 

Set 25 upon B to 47 (G. Pt.) upoii A ; and against 4 
on D is 53-16 lbs. on C. 

6. What is the weight of a short-linked chain 3d 
yards in length, and -j^ths of an inch in diameter ? 

Set 30 upon B to 52 (G, Pt.) upon A} and against 6 on 
D is 29-5 lbs. on O, 



zzi/ 



Ht«-r/"«ftiif--^"^ ■'v'S: ,■■ t IB,;:', •■ ; f : -7 -V • rs~ r 



50 INSTRUMENTAL RULES. 



LAND SURVEYING. 

If the dimensions taken are in chains, the gauge- 
point is 1 or 10 ; if in perches, 160 ; and if in yards, 
4840. 

Rale. — Set the length upon B to the gauge-point 
on A ; and against the breadth upon A is the content 
in acres upon B. 

1. Required the number of acres or contents of a 
field 20 chains 50 links in length, and 4 chains 40 links 
in breadth. 

Set 20*5 on B to 1 on A ; and against 4-4 on A is 9 acres on B. 

2. In a piece of ground 440 yards long, and 44 
broad, how many acres? 

Set 440 upon B to 4840 on A ; and against 44 on A is 4 
acres on B. 

Power of steam-engines. 

Condensing Engines. •— Rule. Set 3*5 on C to 10 on 
D ; then t) is a line of diameters for cylinders * and G 
the corresponding number of horses' power; thus, 

H.Pr.3£ 4 5 6 8 10 12 16 20 25 30 40 50 on C. 
O; D. 10 in. 10| 12 13£ 15£ 17 18| 2l£ 24 26| 29£ 33| 37| on D. 

The same is effected on the common rule by setting 
5 on C to 12 on D. 

Non-condensing Engines. — Rule. Set the pressure 
of steam in lbs. per square inch on B to 4 upon A ; and 
against the cylinder's diameter on D is the number of 
horses' power upon C. 

Required the power of an engine, when the cylinder 
is 20 inches diameter and steam 30 lbs. per square 
inch. 

Set 30 on B to 4 on A ; and against 20 on D is 30 horses' 
power on C. 

The same is effected on the common rule by setting 
the force of the steam on B to 250 on Ai 



STRENGTH OF MATERIALS. 



51 



OF ENGINE BOILERS. 

How many superficial feet are contained in a boiler 
23 feet in length and 5-| in width ? 

Set 1 upon B to 23 upon A ; and against 5'5 upon B is 
126'5 square feet upon A. 

If 5 square feet of boiler surface be sufficient for 
each horse -power, how many horses' power of engine 
is the boiler equal to ? 

Set 5 upon B to 126-5 upon A ; and against 1 upon B 
is 25*5 upon A. 



STRENGTH OF MATERIALS. 



Materials of construction are liable to four differ- 
ent kinds of strain, viz., stretching, crushing, transverse 
action, and torsion, or twisting : the first of which de- 
pends upon the body's tenacity alone ; the second, on 
its resistance to compression ; the third, on its tenacity 
and compression combined; and the fourth, on that 
property by which it opposes any acting force tending 
to change from a straight line, to that of a spiral direc- 
tion, the fibres of which the body is composed. 

In bodies, the power of tenacity and resistance to 
compression, in the direction of their length, is as the 
cross section of their area multiplied by the results of 
experiments on similar bodies, as exhibited in the fol- 
lowing table. 

5* 



52 STRENGTH OF MATERIALS. 




Table showing the Tenacities, Resistances to Compres- 
sion, and other Properties of the common Materials 
of Construction. 


- 


Names of Bodies. 


Absolute. 


Compared with Cast Iron. 




Tenacity 
in lbs. 
per eq,. 
inch. 


Resistance 
to compres- 
sion in lbs. 
per sq. in. 


Its 

strength 
is 


Its exten- 
sibility 
is 


Its 

stiffness 
is 


Ash, 


14130 


.... 


0-23 


2-6 


0-089 




Beech, 


12225 


8548 


0-15 


2-1 


0-073 






Brass, 


17968 


10304 


0-435 


0»9 


0-49 






Brick, 


275 


562 


... 


. . 


... 






Cast Iron, .... 


13434 


86397 


1-000 


1-0 


1-000 






Copper,(wrOught) 


33000 














Elm, 


9720 


1033 


0-21 


2-9 


0-073 






Fir, or Pine, white 


12346 


2028 


0-23 


2-4 


0-1 






" " " red. 


11800 


5375 


0-3 


2-4 


0-1 






« " " yellow 


11835 


5445 


0-25 


2-9 


0-087 






Granite, Aberdeen 


. . . 


10910 


... 


. , 


... 






Gun-metal, (cop- 
















per 8, and tin 1.) 


35838 


.... 


0-65 


1-25 


0-535 






Malleable Iron, . 


56000 


.... 


1-12 


0-86 


1-3 






Larch, 


12240 


5568 


0-136 


2-3 


0-058 






Lead, 


1824 


.... 


0-096 


2-5 


0-0385 






Mahogany, Hond. 


11475 


8000 


0-24 


2-9 


0-487 






Marble, 


551 


6060 


. . . 


. . 


. . 






Oak, 


11880 


9504 


• 0-25 


2-8 


0-093 






Rope, (lin.incir.) 


200 


.... 


. . . 


. . 


. . 






Steel, 


128000 


.... 


. . . 


. . 


, . 






Stone, Bath, . . . 


478 


.... 


. . . 


. . 


, . 






" Craigleith, 


772 


5490 


. . . 


. . 


. . 






" Dundee, . 


2661 


6630 


. . . 


. . 


. . 






" Portland, . 


857 


3729 


. . . 


. . 


. . 






Tin, (cast) .... 


4736 


.... 


0-182 


0-75 


0-25 






Zinc, (sheet). . . 


9120 


.... 


0-365 


0-5 


0-76 




L. — — . 





STRENGTH JOF MATERIALS. 



53 



COOOOD^JTC5C»Ot^CO. 
>tt|l- , H» '*3!i-'44» »*-|>— 'colt— ' 


Circum-of rope 
in inches. 


*- CO CR i-* © -a C* ^ to 


Weight per 
fathom, in lbs. 


£k^H roi ^j°^H<h 


Diameter of 
chain, in inches. 


CO OS tC tO M M M 

-^ to 'i Id GO rf>> O 00 C» 


. Weight per 
fathom, in lbs. 


OD -J © Cs ♦£»• C* bO »-» h-» 1 f 5- 

Cv-I^t0 05 0iOC5 0i ^&4 


• flSCft^OSCOtpwOO 


Circum. of rope 
in inches. 


C5Csi^^WCOWN2W 
OffiODO(CCQOCOCO 


Weight per 
fathom, in lbsu 


«r «i a «r s£>!-* 


Biameter of 
chain, in inches. 


-t— ' 

ffi05^0t- , 05 0ffl05 


Weight per 
fathom, in lbs. 


tO tO IO M H M M M M 
^tO©QD©^C0»-»© 

QDOOODM+^QDOOMO 


ft! 



I 

3 



| 



A. 

I 



^ 

& 
>§ 



Note. — It must be understood and also borne in mind 
£hat, in estimating the amount of tensile strain to which a 
body is subjected, the weight of the body itself must also be 
taken into account; for according to its position so may it 
approximate to its whole weight, in tending to produce 
extension within itself; as in the almost constant applica- 
tion of ropes and chaias to great depths, considerable 
heights, &c- * 



54 



STRENGTH OF MATERIALS. 



Alloys that are of greater Tenacity than the Sum of 
their Constituents, as determined by the Experiments 
of Muschenbroek. 

Swedish copper 6 pts„ Malacca tin 1 ; tenacity per sq. inch, 64,000 lbs. 



Chili copper 6 parts, Malacca tin 1 ; 
Japan copper 5 parts, Banca tin 1 ; 
Anglesea copper 6 parts, Cornish tin 1 ; 
Common block-tin 4, lead 1, Zinc 1 ; 
Malacca tin 4, regulus of antimony 1 ; 
Block tin 3, lead I ; 
Block tin 8, zinc 1 ; 
Lead 1, zinc 1 ; 



60,000 
57,000 
41,000 
13,000 
.12,000 
10,200 
10,000 
4,500 



RESISTANCE TO LATERAL PRESSURE, OR TRANSVERSE 
ACTION. 

The strength of a square or rectangular beam to re- 
sist lateral pressure, acting in a perpendicular direction 
to its length, is as the breadth and square of the depth, 
and inversely as the length; — thus, a beam twice the 
breadth of another, all other circumstance's being alike, 
equal twice the strength of the other ; or twice the 
depth, equal four times the strength, and twice the 
length, equal only half the strength, &c, according to 
the rule. 



Table of Data, containing the Results of Experiments 
on the Elasticity and Strength of various Species of 
Timber, by Mr. Barlow. 



Species of Timber. 


Value 
of E. 


Value 
of S. 


Species of Timber. 


Value 
of E. 


Value 
of S. 


Teak .... 


174-7 


2402 


Elm .... 


50-64 


1013 


Poona . . . 


122-20 


2221 


Pitch pine . . 


88- (IS 


1032 


English Oak . 


105 


1072 


Red pine . . 


133 


1341 


Canadian do . 


155-5 


1760 


New England fir 


158-5- 


1102 


Dantzic do . 


86-2 


1457 


Riga fir . . . 


90 


1100 


Adriatic do . 


70-5 


1383 


Mar Forest do 


63 


1200 


Ash . . . 


119 


2026 


Larch . . . 


70 


900 


Beech . . . 


98 


1550 


Norway spruce 


105-47 


1474 



STRENGTH OF MATERIALS, 



55 



To find the dimensions of a beam capable of sustain- 
ing a given iveight, with a given degree of deflection, 
when supported at both ends. 

Rule. — Multiply the weight to be supported in lbs. 
by the cube of the length in feet ; divide the product 
by 32 times the tabular value of E, multiplied into the 
given deflection in inches ; and the quotient is the 
breadth multiplied by the cube of the depth in inches. 

Note 1. — When the beam is intended to be square, then the 
fourth root of the quotient is the breadth and depth required. 

Note 2. — If the beam is to be cylindrical, multiply the 
quotient by 1'7, and the fourth root of the product is the 
diameter. 

Ex. The distance between the supports of a beam 
of Riga fir is 16 feet, and the weight it must be capa- 
ble of sustaining in the middle of its length is 8000 
lbs., with a deflection of not more than £ of an inch ; 
what must be the depth of the beam, supposing the 
breadth 8 inches ? 

H | '^rj- 5 = 15175 -f 8 = Vl89T= 12-35 in., the depth. 

To determine the absolute strength of a rectangular 
beam of timber, when supported at both ends, and load- 
ed in the middle of its length, as beams in general ought 
to be calculated to, so that they may be rendered capa- 
ble of withstanding all accidental cases of emergency. 

Rule. — Multiply the tabular value of S by four 
times the depth of the beam in inches, and by the area 
of the cross section in inches ; divide the product by 
the distance between the supports in inches, and the 
quotient will be the absolute strength of the beam in lbs. 

Note 1. — If the beam be not laid horizontally, the-distance 
between the supports, for calculation, must be the horizontal 
distance. 

Note 2. — One fourth of the weight obtained by the rule, 
is the greatest weight that ought to be applied in practice aa 
permanent load. 



oh STRENGTH OF MATERIALS. 

Note 3. — If the load is to be applied at any other point 
than the middle, then the strength will be as the product of 
the two distances is to the square of half fche length of the 
beam between the supports ;-^or, twi^e the distance from 
one end, multiplied by twice from the other, and divided by 
the whole length, equal the effective length of the beam. 

Ex. In a building 18 feet in width, an engine boiler 
of 54 tons is to be fixed, the centre of which to be 7 
feet from the wall $ and having two pieces of red pine, 
10 inches by 6, which I can lay across the two walls 
for the purpose of slinging it at each end, — may I 
with sufficient confidence apply them, so as to effect 
this object ? 

2240x5-5 c1flA1 , , , j 

— ^ — ss 6160 lbs. to carry at each end. 

And 18 feet — 7 = 11, double each, or 14 and 22, then 
14 x 22 
— ^-— as 17 feet, or 204 inches, effective length of beam. 

Tabular value of S, red pine, « 1341 X * * 10 X 60 -^ 15776 lbs. 
the absolute strength of each piece of timber at that point. 

To determine the dimensions of a rectangular bmni 
capable of supporting a required weight, with a given 
degree of defection, when fixed at one end. 

Rule. — Divide the weight to be supported, in lbs., 
by the tabular value of E, multiplied by the breadth 
and deflection, both in inches ; and the cube root of 
the quotient, multiplied by the length in feet, equal 
the depth required in inches. 

Ex, A beam of ash is intended to bear a load of 700 
lbs. at its extremity ; its length being 5 feet, its breadth 
4 inches, and the deflection not to exceed \ of an inch. 

Tabular value of E = 119 X 4 X -5^238 the divisor j 
then 700 -f 238 — Sv^^oTx 5=7*25 in., depth of the beam. 



-STRENGTH OF MATERIALS* 



57 



To find the absolute strength of a rectangular bearn^ 
when fixed at one end, and loaded at the other* 

Ride, — Multiply the value of S by the depth of the 
bean), and by the area of its section, both in inches $ 
divide the product by the leverage in inches, and 
the quotient equal the absolute strength of the beam 
in lbs. 

Ex, A beam of Riga fir, 12 inches by 4^, and pro* 
jecting 6^ feet from the wall 5 what is the greatest 
weight it will support at the extremity of its length ? 



Tabular value of S =s 1100. 
12 X 4*5 = 54 sectional area* 



Then, 



1100 X 12 X 54 

78 * 



= 9138-4 lbs. 



When fracture of a beam is produced by vertical 
pressure, the fibres of the lower section of fracture are 
separated by extension, whilst at the same time those 
of the upper portion are destroyed by compression ; 
hence exists a point in section where neither the one 
nor the other takes place, and which is distinguished 
as the point of neutral axis. Therefore, by the law of 
fracture thus established, and proper data of tenacity 
and compression given, as in the table, (p. 52) we are 
enabled to form metal beams of strongest section with 
the least possible material. Thus, in cast iron, the resis- 
tance to compression is nearly as 6£ to 1 of tenacity ; 
consequently a beam of cast iron, to be of strongest 
section, must be of the following form, 
and a parabola in the direction of its 
length, the quantity of material in the 
bottom flange being about 6£ times that 
of the upper. But such is not the case with beams of 
timber ; for although the tenacity of timber be on an 
average twice that of its resistance to compression, its 
flexibility is so great, that any considerable length of 
beam, where columns cannot be situated to its support, 




58 



STRENGTH OF MATERIALS, 



requires to be strengthened or trussed by iron rod&, as 
in the following manner. 




And these applications of principle not only tend to 
diminish deflection, but the required purpose is also 
more effectively attained, and that by lighter pieces of 
timber. 

To ascertain the absolute strength of a cast iron 
beam of the preceding form, or that of strongest 
section. 

Rule. — Multiply the sectional area of the bottom 
flange in inches by the depth of the beam in inches, 
and divide the product by the distance between the 
supports, also in inches; and 514 times the quotient 
equal the absolute strength of the beam in cwts. 

The strongest form in which any given quantity of 
matter can be disposed is that of a hollow cylinder ; 
and it has been demonstrated that the maximum of 
strength is obtained in cast iron, when the thickness 
of the annulus, or ring, amounts to \ of the cylinder's 
external diameter ; the relative strength of a solid to 
that of a hollow cylinder being as the diameters of 
their sections. 



STRENGTH OF MATERIALS. 



59 



A Table showing the Weight or Pressure a Beam of 
Cast Iron, 1 inch in breadth, will sustain, without 
destroying its elastic force, when it is supported at 
each end, and loaded in the middle of its length, and 
also the deflection in the middle which that weight 
will produce. By Mr. Hodgkinson, Manchester. 



Length. 


6 feet. 


7 feet. 


8 feet. 


feet. 


10 feet. 


Depth 


Weight 


Defl. 


Weight 
in lbs. 


Defl. 


Weight 


Defl. 


Weight 


Defl. 


Weight 


Defl. 


in in. 


in lbs. 


in in. 


in in. 


in lbs. 


in in. 


in lbs. 


in in. 


in lbs. 


in in. 


3 


1278 


•24 


1089 


•33 


954 


•426 


855 


•54 


765 


'66 


3i 


1739 


•205 


1482 


•28 


1298 


•365 


1104 


•46 


1041 


•57 


4 


2272 


•18 


1936 


•245 


1700 


•32 


1520 


•405 


1300 


•5 


*h 


2875 


•16 


2450 


•217 


2146 


•284 


1924 


•36 


1721 


•443 


5 


3560 


•144 


3050 


•190 


2650 


•256 


2375 


•32 


2125 


•4 


6 


5112 


•12 


4356 


•163 


3816 


•213 


3420 


.27 


3000 


•33 


7 


6958 


•103 


5929 


•14 


5194 


•183 


4655 


•23 


4165 


•29 


8 


9088 


•09 


7744 


•123 


6784 


•16 


6080 


•203 


5440 


•25 


9 


— 


— 


9801 


•109 


8586 


•142 


7695 


•18 


6885 


•22 


10 


— 


— 


12100 


•098 


10600 


•128 


9500 


•162 


8500 


•2 


11 


— 


— 


— 


— 


12826 


•117 


11495 


•15 


10285 


•182 


12 


— 


— 


— 


— 


15264 


•107 


13080 


•135 


12240 


•17 


13 


— 


— 


— 


— 


— 


— 


16100 


•125 


14400 


•154 


14 
6 


— 


— 


— 


— 


— 


— 


18600 


•115 


10700 


•143 


12 feet. 


14 feet. 


16 feet. 


18 feet. 


20 feet. 


2548 


•48 


2184 


•65 


1912 


•85 


1699 


1-08 


1530 


1-34 


7 


3471 


•41 


2975 


•58 


2603 


•73 


2314 


•93 


2082 


1-14 


8 


4532 


•36 


3884 


•49 


3396 


•64 


3020 


•81 


2720 


1-00 


9 


5733 


•32 


4914 


•44 


4302 


•57 


3825 


•72 


3438 


•89 


10 


7083 


•28 


6071 


•39 


5312 


•51 


4722 


•64 


4250 


•8 


11 


8570 


•26 


7346 


•36 


6428 


•47 


5714 


•59 


5142 


•73 


12 


10192 


•24 


8736 


•33 


7648 


•43 


6796 


•54 


6120 


•67 


13 


11971 


•22 


10260 


•31 


8978 


•39 


7980 


•49 


7182 


•61 


14 


13883 


•21 


11900 


•28 


10412 


•36 


9255 


•46 


8330 


•57 


15 


15937 


•19 


13660 


•26 


11952 


•34 


10624 


•43 


9562 


•53 


16 


18128 


•18 


15536 


•24 


13584 


•32 


12080 


•40 


10880 


'5 


17 


20500 


•17 


17500 


•23 


15353 


•3 


13647 


•38 


12282 


•47 


18 


22932 


•16 


19656 


•21 


17208 


•28 


15700 


•36 


13752 


•44 



Note. — This Table shows the greatest weight that ever 
ought to be laid upon a beam for permanent load ; and, if 
there be any liability to jerks, &c, ample allowance must be 
made ; also, the weight of the beam itself must be included. 

6 



60 STRENGTH OF MATERIALS. 

To find the weight of a cast iron beam of given 
dimensions* 

Rule* — Multiply the sectional area in inches by the 
length in feet, and by 3»2, the product equal the weight 
in lbs. 

Ex. Required the weight of a uniform rectangular 
beam of cast iron, 16 feet in length, 11 inches in 
breadth, and 1^ inch in thickness. 

11 X 1-5 X 16 X 3-2 a 844 '8 lbs. 

Resistance of Bodies to Flexure by vertical Pressure. 

When a piece of timber is employed as a column or 
support, its tendency to yielding by compression is dif- 
ferent according to the proportion between its length 
and area of its cross section ; and supposing the form 
that of a cylinder whose length is less than seven or 
eight times its diameter, it is impossible to bend it by 
miy* force applied longitudinally, as it will be destroyed 
by splitting before that bending can take place ; but 
when the length exceeds this, the column will bend 
under a certain load, and be ultimately destroyed by 
a similar kind of action to that which has place in the 
transverse strain. 

Columns of cast iron and of other bodies are also 
similarly circumstanced, this law having recently been 
fully developed by the experiments of Mr. Hodgkinson 
on columns of different diameters, and of different 
lengths. 

When the length of a cast iron column with flat 
ends equals about thirty times its diameter, fracture 
will be produced wholly by bending of the material. 
When of less length, fracture takes place partly by 
crushing and partly by bending. But, when the col- 
umn is enlarged in the middle of its length from one 
and a half to twice its diameter at the ends, by being 
cast hollow, the strength is greater by ^th than in a 
solid column containing the same quantity of material. 



STRENGTH OF MATERIALS. 61 



To determine the dimensions of a support or column 
to bear, without visible curvature, a given pressure in 
the direction of its axis. 

Rule.-**- Multiply the pressure to be supported in 
lbs. by the square of the column's length in feet, and 
divide the product by twenty times the tabular value 
of E ; and the quotient will be equal to the breadth 
multiplied by the cube of the least thickness, both 
being expressed in inches. 

Note 1.— When the pillar or support is a square, its side 
will be the fourth root of the quotient. 

2. If the pillar or column be a cylinder, multiply the 
tabular value of E by 12, and the fourth root of the quotient 
equal the diameter. 

Ex. 1. What should be the least dimensions of an 
oak support, to bear a weight of 2240 lbs. without 
sensible flexure, its breadth being 3 inches, and its 
length 5 feet ? 

Tabular value ofEs 105, 

Ex. 2. Required the side of a square piece of Riga 
fir, 9 feet in length, to bear a permanent weight of 
6000 lbs. 

Tabular value of E = 96, 

, 6000 X 9 2 4 /nZo- a • i. i 

and -s 7 r — g^ = W 253 = 4 inches, nearly. 



_- 



62 



STRENGTH OF MATERIALS. 



IS 



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<M 

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o 

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STRENGTH OF MATERIALS. 



63 



Practical Utility of the preceding Table. 

Ex. Wanting to support the front of a building with 
cast iron columns 18 feet in length, 8 inches in diam- 
eter, and the metal 1 inch in thickness ; what weight 
may I confidently expect each column capable of sup- 
porting without tendency to deflection ? 

Opposite 8 inches diameter and under 18 feet = 1097 
Also opposite 6 in. diameter and under 18 feet = 440 

= 657 cwt. 

Note. — The strength of cast iron as a column being 1-0000 
" steel " =2-518 

" wrought iron " = 1*745 

" (oak) Dantzic " = -1088 

" red deal " - -0785 



Elasticity of Torsion, or Resistance of Bodies to 
Twisting. 

The angle of flexure by torsion is as the length and 
extensibility of the body directly and inversely as the 
diameter ; hence, the length of a bar or shaft being 
given, the power, and the leverage the power acts Avith, 
being known, and also the number of degrees of tor- 
sion that will not affect the action of the machine, to 
determine the diameter in cast iron with a given angle 
of flexure. 

Rule. — Multiply the power in lbs. by the length of 
the shaft in feet, and by the leverage in feet ; divide 
the product by fifty-five times the number of degrees 
in the angle of torsion ; and the fourth root of the 
quotient equal the shaft's diameter in inches. 

Ex. Required the diameters for a series of shafts 
6* 



64 MECHANICS. 

35 feet in length, and to transmit a power equal to 
1245 lbs., acting at the circumference of a wheel 2^ 
feet radius, so that the twist of the shafts on the appli- 
cation of the power may not exceed one degree. 

1245 X 35 X 2-5 r-^- _ „ . , . ,. 

k« — r* = V 19 81 = 6*67 inches in diameter. 

55 X 1 » 



Relative Strength of Metals to resist Torsion. 



Cast Iron, = 1* 

Copper, = -48 

Yellow Brass, . . . = -511 
Gun metal, =s '55 



Swedish bar iron, . . =1*05 
English " " . . = 1-12 

Sheer steel, = 1-96 

Cast " =2-1 



MECHANICS. 

PRELIMINARY REMARKS. 

Mechanics, regarded as a science, comprehends the 
sum of our knowledge relative to the sensible motions 
of bodies either actually existing or expressed by the 
opposition of forces tending to produce motion. The 
science is thus resolvable into a code of discovered laws, 
applying to the causes which occasion and modify the 
direction and the velocities of motion, and is there- 
fore distinct from those branches of science in which, 
although presenting phenomena of motion in sensible 
portions of matter, we do not consider the circum- 
stances and laws of these motions, but only the effects 
produced. 

When motion itself is considered, the reasoning be- 



MECHANICS. 



65 



longs to mechanics, and it is probable that as our knowl- 
edge of the laws which govern the phenomena that are 
evolved under the hand of the experimental philosopher 
becomes more extended, a wider meaning will be given 
to the science of motion. The definition which is here 
given of mechanics is not coeval with the name. The 
science, like most other sciences, has gradually ex- 
panded to its present extent. It was originally the 
science of machines — these being the first subjects 
of its speculation ; and, as every material combination 
employed for producing or preventing motion may be 
regarded as a machine, and may be resolved into the 
same elementary principles as those employed in ma- 
chines, — the mechanical powers, — the name " me- 
chanics " came to be applied to motion, the tendency 
to motion of any bodies whatever. Mechanics still 
continues to be defined by some the science of force, 
and there does not appear to be any valid objection to 
the definition. Force is the cause of motion, and its 
laws are identical with the laws of motion ; and, con- 
sequently, the science of force coincides, in all its parts, 
with the science of motion, which is mechanics. 



ELEMENTS OP MACHINERY. 

THE LEVER. 



To produce mechanical effects, it is rarely conven- 
ient to apply directly our available force, — meaning 
by mechanical effect, moving a body of a certain weight 
through a certain space, — the assistance of machinery 
is required. In fact, the essential idea of machinery 
is, that it renders force available for effecting certain 
practical ends. Machines prepare, as it were, the raw 



66 MECHANICS. 

material of force supplied to us from natural sources. 
It is transmitted and modified by certain combinations 
of the elements of machinery, and is given off, at last, 
in a condition suitable for producing the desired me- 
chanical effect. We do not create force ; the end of 
machinery is just to transmit it, and diffuse or concen- 
trate it in one or more points of action. The various 
diffused or concentrated forces, then, being added to- 
gether, will just amount to the original available force. 

All machinery, when analyzed, will be found to con- 
sist of a combination of six simple machines, or ele- 
ments, commonly called mechanical powers. This term 
is not correctly applied to these elements. They are 
not powers, or, in other words, sources of power or 
force ; they simply transmit and diffuse or concentrate 
forces. These six elements are, the lever, the pulley, 
the ivheel and axle, the inclined plane, the wedge, and 
the screw. 

To understand, therefore, the nature of any machine, 
a correct idea of these elements is requisite. 

A lever is an inflexible rod, by the application of 
which one force may balance or overcome another. 
These forces are termed, respectively, the power and 
the resistance, or weigld, not from any difference in 
the action of the forces, but with reference merely to 
the intention with which the machine is used ; and 
indeed the same terms are used about all the other 
mechanical elements. In applying the rod to operate 
upon any resistance, it must rest upon a centre prop, 
or fulcrum, somewhere along its length, upon which it 
turns in the performance of its work. Thus, there are 
three points in every lever, to be regarded in examin- 
ing its action, namely, the two points of application 
of the power and the weight, and the point resting 
on the fulcrum. There is a certain relation to be ob- 
served between the magnitudes of the opposing force, 
and their distances from the fulcrum, namely, that, in 
every case, the power, multipled by its distance from 



Mechanics. 



67 



the fulcrum, is equal to the weight, multiplied by its 
distance from the same point. From this, simple 
rules may be deduced for calculation. 

To know the poWer to be applied, at a certain dis- 
tance from the fulcrum, to overcome a resistance acting 
also at a certain distance, multiply the resistance by its 
distance from the fulcrum, which gives its moment, and 
divide the product by the distance given. Quotient 
will be the power, it being observed that the distance 
and the force be each expressed in the same unit of 
measure. For example, a weight, 1120 lbs., at 3 inches 
from the fulcrum, is to be balanced by a force at the dis- 
tance of 10 feet. Now 10 feet are equal to 120 inches ; 
and the moment of 1120 lbs. is 1120 X 3=r3360. 
Divide this by 120, we have 28 lbs. for the power 
required. 

Again : to know the distance at which a given force 
ought to be applied to balance a given weight at a 
certain distance, we must, in like manner, multiply the 
weight by its distance, as before, and divide by the 
given power. 1120 lbs., for example, at 3 inches dis- 
tance, are to be balanced by a force of 28 lbs. To 
find the distance of this weight, 1 120 lbs. multiplied 
by 3, give 3360, which, divided by 28, give 120 
inches, or 10 feet. 

tHE WHEEL AND AXLE, OR CRANE. 

The mechanical advantage of the wheel and axle, or 
crane, is as the velocity of the weight to the velocity 
of the power ; and, being only a modification of the 
first kind of lever, it of course partakes of the same 
principles. 

To determine the amount of effective power produced 
from a given power, by means of a crane with known 
peculiarities. 

Rule. — Multiply together the diameter of the circle 
described by the handle and the number of revolutions 



- w. .1 . .. 



68 MECHANICS. 

of the pinion to one of the wheel; divide the product by 
the barrel's diameter in equal terms of dimensions ; and 
the quotient is the effective power to 1 of exertive force. 
Ex. Let there be a crane, the handle of which 
describes a circle of 30 inches in diameter ; the pinion 
makes 8 revolutions for 1 of the wheel, and the barrel 
is 11 inches in diameter; required the effective power 
in principle, also the weight that 36 lbs. would raise, 
friction not taken into account. 

30x8 =£ 21-9 to 1 of exertive force, and 21-9 X 36 * 785'5 lbs. 
11 

Given any two parts of a crane, to find the third that 
shall produce any required proportion of mechanical 
effect. 

Rule. — Multiply the two given parte together, and 
the quotient is the dimensions of the other parts in 
equal terms of unity. 

Ex. Suppose that a crane is required, the ratio of 
power to effect being as 40 to 1, and that a wheel and 
pinion 11 to 1 is unavoidably compelled to be em- 
ployed ; also the throw of each handle to be 16 inches : 
what must be the barrel's diameter, on which the rope 
or chain must coil ? 

16 X 2 = 32 inches diameter described by the handle. 
And 32 X 11 = 8"8 inches, the barrel's diameter. 
40 

THE PULLEY 

The principle of the pulley, or more practically tne 
block and tackle, is the distribution of weight on 
various points of support ; the mechanical advantage 
derived depending entirely upon the flexibility and ten- 
sion of the rope, and the number of pulleys or sheives 
in the lower or rising block. Hence, by blocks and 
tackle of the usual kind, the power is to the weight 



Villi *»-i rWiniYT.1 'Tit, 



MECHANICS. 69 

as the number of cords attached to the lower block ; 
whence the following rules : — - 

1. Divide the weight to be raised by the number of 
cords leading to, from, or attached to the lower block ; 
and the quotient is the power required to produce an 
equilibrium, provided friction did not exist. 

2. Divide the weight to be raised by the power to be 
applied ; the quotient is the number of sheives in, or 
cords attached to, the rising block. 

Ex. 1. Required the power necessary to raise a 
Weight of 3000 lbs. by a four and five sheived block and 
tackle, the four being the movable or rising block. 

Necesarily, there are nine cords leading to and 
from the rising block ; — 

Consequently, — ~ — = 333 lbs., the power required. 

Ex. 2. I require to raise a weight 4256 lbs. ; the 
amount of my power to effect this object being 500 
lbs. What kind of block and tackle must I, of neces- 
sity, employ ? 

-^—- as 8*51 cords — of necessity, there must be 4 sheives, 
or 9 cords, in the rising block. 

As the effective power of the crane may, by addi- 
tional wheels and pinions, be increased to any required 
amount, so may the pulley and tackle be similarly 
augmented by purchase upon purchase. Two of the 
most useful are known by the term runner and tackle, 
and the second by that of Spanish burton. 





70 


THE INCLINED PLANE. 






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Note. — Alth 
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ough this table has been calculated partici 
ges on railway inclines, it may with equ 
>plied to any other incline, the amount o 
vel being known. 


I- 

f 



THE INCLINED PLANE. 71 



•Application of the preceding Table. 

1. What weight will a tractive power of 150 lbs. 
draw up an incline of 1 in 340, the resistance on the 
level being estimated at g-J^th part of the insistent 
weight ? 

In a line with 40 in the left-hand column and under 

200 is GO!!? 

Also, in the same line and under 300 is -00294 

Added together = 0071 1 

Then = 2101)7 lhs. weight drawn up the plane 

■00711 

2. What weight would a force of 150 lbs. c;aw down 
the same plane, the friction on the level be7jl£ Ae same 
as before ? 

Friction on the level - • -00117 
Gravity of the plane =-'00294 subtract 

= -00:23 

And — - — = 121915 lbs. weight dr .wn down the plane. 
•001-23 



Example of Incline when Velocity is taken info Jlccount 

A power of 280 lhs. at a velocity of 75 feet per min-- 
ute,i3 to he enployed for moving weights up an inclined 
plane 12 feet -, n height and 163 feet in length, the least 
velocity of the weight to De 8 feet per minute ; required 
the greatest weight that the power is equal to. 

230 x 75 x 163 2811750 __ ■ „ ,„ _„ , 

= = 29288 lbs., or l3-2o tons 

12X8 



72 



MECHANICS. 



THE INCLINED PLANE. 

The inclined plane is the representative of the second 
class of mechanical elements. Its fundamental law of 
action is that of the composition and resolution of forces. 
The manner in which the advantage is immediately c.e- 
rived from it is, therefore, distinct from that of the first 
class ; there is necessarily a fulcrum, a point round 
which all the motion takes place, and through which 
the power acts on the resistance ; whereas, in this class, 
there is no apparent centre of action. The advantage 
gained by the inclined plane, when the power acts in a 
parallel direction to the plane, is as the length to the 
height or angle of inclination. Hence the rule. Divide 
the weight by the ratio of inclination, and the quotient 
equal the power that will just support that weight upon 
the plane. Or, multiply the weight by the height of 
the plane, and divide by the length — the quotient is 
the power. 

Ex. Required the power or equivalent weight capa 
ble of supporting a load of 350 lbs. upon a plane of 1 in 
12, or 3 feet in height and 3G feet in length. 

350 350 X 3 

■ — = 29 16 lbs., or =29*16 lbs. power, as before 

12 S6 



THE WEDGE. 



The wedge is a double inclined plane ; consequently, 
its principles are the same. Hence, when two bodies 
are forced asunder by means of the wedge, in a direction 
parallel to its head, multiply the resisting power by 
half the thickness of the head or back of the wedge, and 
divide the product by the length of one of its inclined 
sides ; the quotient is the force equal to the resistance. 

Ex. The breadth of the back or head of a wedge 
being 3 inches, its inclined sides each 10 inches, re 



MECHANICS. 73 

quired the power necessary to act upon the wedge so as 
to separate two substances whose resisting force is 
equal to 150 lbs 

L^xi2 = 2 ,.. 51b , 

10 

A'ote. — When only ore of the bodies is movable, the whole 
breadth of the wedge is .aken for the multiplier. 



THE SCREW. 

The screw is another modification of the inclined 
plane, and it may be said to remove the same kind of 
practical inconveniences incidental to the use of the 
latter, that the pulley does in reference to the simple 
lever. The lever is very limited in the extent of its 
action ; so is the inclined plane. But the pulley multi- 
plies the extent of the action of the lever, by presenting 1 , 
in effect, a series of levers acting in regular succession; 
and just such a purpose is effected by the screw. It 
multiplies the extent of the action of the inclined plane, 
by presenting, in effect, a continued series of planes. 

The screw, in principle, is that of an inclined plane 
wound round a cylinder, which generates a spiral of 
uniform inclination, each revolution producing a rise 
or traverse motion equal to the pitch of the screw, or 
distance between the two consecutive threads, — the 
pitch being the height or angle of inclination and the 
circumference the length of the plane. Hence, the me- 
chanical advantage is, as the circumference of the circle 
described by the lever where the power acts is to the 
pitch of the screw, so is the force to the resistance in 
principle. 

Ex. Required the effective power obtained by a 
Bcrew of I inch pitch, and moved by a force equal to 
50 lbs. at the extremity of a lever 30 inches in length, 

0X2x3- 1416x50 

— — -= lft/oO lbs. 

87fi 



4 MECHANICS. 

Ex. 2. Required the power necessary to ovjj-crr-tt a 

resistance equal to 7000 lbs. by a screw of l{ inch piteh 
and moved by a lever 25 inches in length. 

7000x1-25 ; 

= 5a- /3 lbs. power. 

25 x 2 x 3-1416 

In the case of a screw acting on the periphery of a 
toothed wheel, the power is to the resistance as the 
product of the circle's circumference described by the 
winch or lever, and radius of the wheel, to the pro- 
duct of the screw's pitch and radius of the axle or point 
whence the power is transmitted ; but observe that, if 
the screw consist of more than one thread, the apparent 
pitch must be increased so many times as these are 
threads in the screw. Hence, to find what weight a 
given power will equipoise, 

Rule. — Multiply together the radius of the wheel 
the length of the lever at which the power acts, the 
magnitude of the power, and the constant number 
6-2882 ; divide the product by the radius of the axle 
into the pitch of the screw, and the quotient is the 
weight that the power is equal to. 

Ex. What weight will be sustained in equilibria by a 
power of 100 lbs. acting at the end of a lever 24 inches 
in length, the radius of the axle, or point whence the 
power is transmitted being 8 inches, the radius of the 
wheel 14 inches, the screw consisting of a double 
thread, and the apparent pitch equal § of an inch. 

14x24x100x6-2832 .„„„.„ t . ' . . 

= 21111-oo lbs. the power sustained. 

•625 X «2 X 8 

Note. — It is estimated that about one third more power must 
De added, to overcome the fiiction of the screw when loaded, 
than is necessary to constitute a balance between power and 
weight 



CONTINUOUS CIRCULAR 3IOTION. 



OF CONTINUOUS CIRCULAR MOTION 

In mechanics, circular motion is transmitted by means 
of wheels, drums, or pulleys; and accordingly as the 
driving and driven are of equal or unequal diameters, 
so are equal or unequal velocities produced. Hence the 
principle on which the following rules are founded. 

1. When Time is not taken info Account. 

Rule. — Divide the greater diameter, or number of 
teeth, by the lesser diameter or number of teeth ; and 
the quotient is the number of revolutions the lesser will 
make, for one of the greater. 

Ex. How many revolutions will a pinion of 20 teeth 
make, for 1 of a wheel with 125? 

125 -i- 20= G25 or 6| revolutions. 

To fnd the number of revolutions of the last, to one 
if the first, in a train of wheels and pinions. 

Rule. — Divide the product of all the teeth in the 
driving by the product of all the teeth in the driven ; 
and the quotient equal the ratio of velocity required. 

Ex. 1. Required the ratio of velocity of the last, to 1 of 
t*he first, in the following train of wheels and pinions; 
viz., pinions driving, — the first of which contains 10 
teeth, the second 15, and third 18. Wheels driven first, 
15 teeth, second, 25, and third, 112. 

10 x 15 X IB 

. = 225 of a revolution the wheel will make to 

15 X 25 x ->2. 

one of the pinion. 

Ex. 2. A wheel of 42 teeth giving motion to one of 
12, on ^hich shaft is a pulley of 21 inches diameter 

7* 



76 CONTINUOUS CIRCULAR MOTION. 

driving one of 6 ; required the number of revolutions of 
the last pulley to one of the first wheel. 

4^ v 91 . • 

ZZJ2-± = 12-25 or 12£ revolutions. 

12x6 
2. Wlien Time must be regarded. 

Rule. — Multiply the diameter or number of teeth in 
tl\3 driver, by its velocity in any given time, and divide 
the product by the required velocity of the driven ; the 
quotient equal the number of teeth or diameter of the 
driven, to produce the velocity required. 

Ex. 1. If a wheel, containing 84 teeth, makes 20 
revolutions per minute, how many must another contain, 
to work in contact, and make GO revolutions in the 
same time ? 

8 J2^_° = 28 teeth. 
GO 

Ex. 2. From a shaft making 45 revolutions per min- 
ute, and with a pinion 9 inches diameter at the pitch 
line, I wish to transmit motion at 15 revolutions per 
minute ; what, at the pitch line, must be the diameter 
of the wheel. 

= 27 inches. 

15 
Ex. 3. Required the diameter of a puhey to make 16 
revolutions in the same time as one of 24 inches mak- 
ing 36. 

24x36 



: 54 inches. 



16 



The distance between the centres and velocities of tim 
wheels being given, to find their proper diameters. 

Rule. — Divide the greatest velocity by the least; the 
quotient is the ratio of diameter the wheels must beai 
{/) each other. 



CONTINUOUS CIRCULAR MOTION. 7? 

Hence, divide the distance between the centres by 
/lie ratio 4- 1 ; the quotient equal the radius of the 
smaller wheel ; and subtract the radius thus obtained 
from the distance between the centres; the remainder 
equal the radius of the other. 

Ex. 1. The distance of two shafts from centre to 
centre is 50 inches, and the velocity of the one 25 rev- 
olutions per minute, the other is to make 80 in the same 
time ; the proper diameters of the wheels at the pitch 
lines are required. 

50 

80 — 25 = 3-2, ratio of velocity, and = 11-9, the radius 

3-2+1 
of the smaller wheel ; then 50 — 11-9 = 38-1, radius of hrger; 
their diameters are 11-9 x2 =23-8 and 38-1 x 2 = 76-2 inches. 

To obtain or diminish an accumulated velocity by 
means of wheels, pinions, or wheels, pinions, and pulleys, 
it is necessary that a proportional ratio of velocity 
should exist, and which is thus attained : multiply the 
given and required velocities together ; and the square 
root of the product is the mean or pioportionate velo- 
city. 

Ex. Let the given velocity of a wheel containing 54 
teeth equal 16 revolutions per minute, and the given 
diameter of an intermediate pulley equal 25 inches, to 
obtain a velocity of 81 revolutions in a machine ; re- 
quired the .number of teeth in the intermediate wheel 
and diameter of the last pulley. 

•y/31 x 16 = 36 mean velocity. 

51 X 16 nt , 25 = 36 „ , . . 

= 21 teeth and =11-1 inches, diameter of 

36 81 

pulley. 



To determine the proportion of wheels for screw-cut* 
ting by. a lathe. 

In a Jathe properly adapted, screws to any degree of 
oitch, or number of threads in a given length, may he 



/8 CONTINUOUS CIRCULAR MOTION. 

cut by means of a leading screw of any given pitch, ac- 
companied with change wheels and pinions ; coarse 
pitches being effected generally by means of one wheel 
find one pinion with a earner, or intermediate wheel, 
which cause no variation or change of motion to take 
place. Hence the following 

Rvlc. — Divide the number of threads in a given 
length of the screw which is to be cut, by the number 
of threads in the same length of the leading screw at- 
tached to the lathe ; and the quotient is the ratio that 
the wheel on the end of the screw must bear to that on 
the end of the lathe spindle. 

Ex. Let it be required to cut a screw with 5 threads 
in an inch, the leading screw being of £ inch pitch, or 
containing 2 threads in an inch; what must be the ratio 
of wheels applied ? 

5 -f- 2 = 2-5, the ratio they must bear to each other. 

Then suppose a pinion of 40 teeth be fixed upon for 
the spindle, — 

40 X 2-5 = 100 teeth for the wheel on the end of the screw 

But screws of a greater degree of fineness than about 
S threads in an inch are more conveniently cut by an 
additional wheel and pinion, because of the proper de- 
gree of velocity being more effectively attained; and 
these, on account of revolving upon a stud, are com- 
monly designated the stud-wheels, or stud-wheel and 
pinion ; but the mode of calculation and ratio of screw 
are the same as in the preceding rule. Hence, all that 
is further necessary is to fix upon any 3 wheels at 
pleasure, as those for the spindle and stud-wheels; 
then multiply the number of teeth in the spindle-wheel 
by the ratio of the screw, and by the number of teeth in 
that wheel or pinion which is in contact with the wheel 
on the end of the screw; divide the product by the stud- 
wheel in contact with the spindle-wheel ; and the quo- 
tient is the number of teeth required in the wheel on the 
end of the leading screw. 



CONTINUOUS CIRCULAR MOTION. 79 

E.i. Suppose a screw is required to be cut containing 
25 threads in an inch, the leading screw, as before, 
having two threads in an inch, and that a wheel of GO 
teeth is fixed upon for the end of the spindle, 20 for the 
pinion in contact with the screw-wheel, and 100 for thai 
in contact with the wheel on the end of the spindle 
required the number of teeth in the wheel for the end 
oj* the leading screw. 

25-2=12-5, and 6 ° * '- 5x ig = i 5 o tee th. 
100 

Or suppose the spindle and screw-wheels to be thos? 
fixed upon, also any one of the stud-wheels, to find the 
number of teeth in the other. ■ 

60 X 12-5 WA GO X 12-5 x 20 IJWk j _ 

= 20 teeth, or js 100 teeth. 

160 x 100 ISO 



80 



CONTINUOUS CIRCULAR MOTION 



Table of Change Wheels for Screw-culling ; the leading 
Screw being of 4 inch pilch, or containing 2 threads in 
an inch. 





Numb.of 




Number of 




Number of 


e 


teeth in 


a 

en 


teeth in 


a 

CO 

X! 


teeth in 








?>** 


^_j 






«j "v 








C 

"a. 


i 

CO 


O) 

Si • 

**& 

<?*3 


c 
■§■ 

CO 


OH 2 

1? 

«1 




CO 


1- w 


i 
■5 
s 
"B, 


11 
Jl 


C 4> 






























•2 c 


fil 


— o> 


J2 O 


* » 


4> j; 


c a 


s^ 




|s 


?- gg 


B u 
c _ 


"2 u 


3 « 

z = 


(B-g 


J! 


II 


Si 


B? 


5* 


If 


is 


Sz 


SI 


£"* 


% ~ 


! 


80 


40 


8* 


40 


55 


20 


60 


19 


50 


95 


20 


J 00 


M 


80 


50 


84 


90 


85 


20 


90 


194. 


80 


120 


20 


130 


14 


80 


60 


8f 


60 


70 


20 


75 


20 


60 


100 


20 


120 


IS 


80 


70 


9.1 


90 


90 


20 


95 


20£ 


40 


90 


20 


90 


2 


80 


90 


3* 


40 


60 


20 


65 


21 


80 


120 


20 


140 


2* 


SO 


90 


10 


60 


75 


20 


80 


22 


60 


110 


20 


120 


24 


80 


100 


104 


50 


70 


20 


75 


224 


80 


120 


20 


150 


2| 


80 


110 


11 


60 


55 


20 


120 


22=f 


80 


130 


20 


140 


3 


80 


120 


12 


90 


90 


20 


120 


233 


40 


95 


20 


100 


3* 


80 


130 


12| 


60 


85 


20 


90 


24 


65 


120 


20 


130 


3* 


80 


140 


13 


90 


90 


20 


130 


25 


60 


100 


20 


150 


3? 


80 


150 


134 


60 


90 


20 


90 


25* 


30 


85 


20 


90 


4 


40 


80 


13$ 


80 


100 


20 


110 


26 


70 


130 


20 


140 


4* 


40 


85 


14 


90 


90 


20 


140 


27 


40 


90 


20 


120 


44 


40 


90 


14* 


CO 


90 


20 


95 


27* 


40 


100 


20 


110 


43 


40 


95 


15 


90 


90 


20 


150 


28* 


75 


140 


20 


150 


5 


40 


100 


16 


60 


80 


20 


120 


28i 


30 


90 


20 


95 


54 


40 


110 


16^ 80 


100 


20 


130 


3? 


70 


140 


20 


150 


6 


40 


120 


164' 80 


110 


20 


120 


32 


30 


80 


20 


120 


64 


40 


130 


17 1 45 


85 


20 


90 


33 


40 


110 


20 


120 


7 


40 


140 


174! 80 


100 


20 


140 


34 


30 


85 


20 


120 


74 


40 


150 


18 40 


60 


20 


120 


35 


60 


140 


20 


150 


8 


30 


120 


18| j 80 


100 


20 


150 


36 


30 


90 


20 


120! 



CONTINUOUS CIRCULAR MOTION. 



Si 



Table by which to determine the Number of Teeth, 01 
Pitch of Small Wheels, by what is commonly called the. 
Manchester Principle. 



Diametral 


Circular 


Diametral 


Circular 


pitch. 


pitch. 


pitch. 


pilch. 
~-349~ 


3 


1-047 


9 


4 


•785 


10 


•314 


5 


•628 


12 


•262 


6 


•524 


14 


224 


7 


449 


16 


•196 


8 


•393 


20 


•157 



Ex. 1. Required the number of teeth that a whee. 
of 10' inches diameter will contain of a 10 pitch. 

16 X 10= 160 teeth, and the circular pitch ±=.-314 inch. 

Ex. 2. What must be the diameter of a wheel, for a 
9 pitch of 126 teeth ? 

126 

— = 14 inches diameter, circular pitcn -349 inch. 
9 
Note. — The pitch is reckoned on the diameter of the^heel 
instead of the circumference, and designated wheels of 8 pitch, 
12 pitch, &c. 

Strength of the Teeth of Cast Iron Wheels at a given 
Velocity. 



Pitch 

lif l-Hh 


Thiclcn-ss 
of leeth 


Breadth 
of l-eth 


Strpn 


rth of teeth 


1 horse-power at 


3 feet per 


4 feet per 


6 feet per 


8 feet per 


in inches 
3-99 


in inches. 


in inches. 


second. 


second. 


secoml. 


second. 


19 


7-6 


20-57 


27-43 


41-14 


54-85 


3-78 


1-8 


7-2 


17-49 


23-32 


34-98 


46-64 


3-57 


1-7 


6-8 


14-73 


19-65 


29-46 


39-28 


3*36 


1-6 


6-4 


12-28 


16*38 


24-56 


32-74 


3-15 


1-5 


6 


1012 


13-50 


20-21 


26-98 


' 2-94 


1-4 


56 


8-22 


10-97 


16-44 


21-92 


2-73 


1-3- 


5'2 


6-58 


8-78 


13-16 


17-54 


2-52 


1-2 


■ 4-8 


5-18 


6-91 


10-36 


13-81 


» 2-31 


1-1 


4-4 


3-99 


5-32 


7-98 


10-64 


. 2-1 


1-0 


4 


3-00 


4-00 


6-00 


8-00 


I 1 -89 


•9 


3-6 


2-18 


2-91 


4-36 


5-81 


1 63 


•8 


3-2 


1-53 


2-04 


3-06 


3-08 


1 1-47 


•7 


2-8 


1-027 


1-37 


2-04 


2-72 


• 1-26 


•G 


2-4 


•64 


•86 


1-38 


1-84 


, 1-05 


•5 


2 


•375 


•50 


75 


1-00 
— 1 



82 ritAci (,AL PUBERTIES OF WATER. 



PRACTICAL PROPERTIES OF WATER 



By analysis it is ascertained, that water is composed 
of the gases oxygen and hydrogen in a state of chemical 
anion ; its distinguishing properties, like that of othei 
liquids, being nearly incompressible gravity, capability 
of flowing, and constant tendency to press outwards in 
every direction ; also that of being easily changed by 
the absorption of caloric to an aeriform state of any re- 
quired density or degree of elastic force: hence the 
principle of the hydraulic press, the water-wheel, the 
steam engine, &c 

Effects produced by Water in its natural State. 

Because of liquids possessing the properties of gravity 
and capability of flowing freely in every direction, sides 
of wpsels, flood-gates, sluices, &c, sustain a pressure 
equal to the product of the area multiplied by half- the 
depth of the fluid, and by its gravity in equal terms of 
unity. 

But when a sluice or opening through which a liquid 
may issue is under any given continued head, the pres- 
sure is equal the product of the area multiplied into the 
height from the centre of the opening to the surface of 
the fluid. 

Ex. 1. Required the pressure of water on the sides 
of a cistern 18 feet in length, 13 in width and 9 in 
depth. 

The terms of measurement or unity are in feet, 1 cubic foot o, 
water = 62-5 lbs.': hence 18 X 9 X 2-J- 13 X 9 X 2 — 558 x 
4-5 x 62- 5 = 156937-5 lbs. weight of water on bottom — IS x 
13x9 X 02-5= 131625 lbs. 

Ex. 2. Required the pressure on a sluice 3 feet square, 
and its centre 30 feet from the surface of the water 

. 3 X 3 X 30 x 62-5 = 16875 lbs. pressure. 



PRACTICAL PnOPEx ii'ES OF WATER. 83 

The weight of water or other fluid is as the quantity 
but the pressure exerted is as the vertical height. Hence, 
us fluids press equally in every direction, any vesseJ 
containing a fluid sustains a pressure equal to as many 
times the weight of the column of greatest height of 
that fluid, as the area of the vessel is to the sectional 
area of the column. 

Ex. Let a cubical vessel, whose sides are each 4 
square feet, have a tube inserted 1 inch in diameter, and 
6 feet in height, and let both vessel and tube be filled 
with water; required the whole weight of the water 
therein contained, and also the whole pressure exerted 
intending to burst the vessel. 

Cubic contents of the vessel = 8 feet, and each foot = 62-5 lbs. ; 

then 62-5 x8 = 500 area of pipe's section = -7854 inches, and 

height 72 inches, also a cubic inch of water = -03617 lbs.; 

hence/7854 x 72 x -03617 = 2 lbs. + 500 = 502 lbs., total 

weight of the water. 
Again ; the whole height of the column = 96 inches ; then -7854 

X % X -03617 = 2*33 lbs., pressure of column on an equal 

in • i i r . a 14 * x 4 x 6 sides 
area. 144 square inches = 1 square loot, and 

•7854 

= 4100-4 times the area of the pipe's diameter in the whole 

surface ; therefore, 4400-4 X 2-33 = 10253 lbs., or total amount 

of pressure exerted. 

To find the velocity of water issuing a circular orifice 
at any given depth from the surface. 

Rule. -Multiply the square root of the height or 
depth to the centre of the orifice by 8-1 ; and the product 
is th.i velocity of the issuing fluid in feet per second. 

Ex. Required the velocity of water issuing through 
an orifice under a head of 11 feet from the surface. 

V 11 = 3-3166 X 8-1 = 26-864 feet, velocity per second 
In the discharge of water by a rectangular aperture in 
the side of a reservoir, and extending to the surface, 
the velocity varies nearly as the square root of the height, 
ana the quantity discharged per second equal frds of 
Jie velocity due to the mean height, allowing for the 
8 



L 



84 PRACTICAL PROPERTIES OF WATER. 

"contraction of the fluid according to the form ot tti* 
opening, which renders the coefficient in this case equal 
to 5-1 ; whence the following general rules. 

1. When the aperture extends to the surface of the 
fluid. Multiply the area of the opening in feet by the 
square root of its depth also in feet, and that product by 
5-1 ; then will §rds of the last product equal the quantity 
discharged, in cubic feet, per second. 

2. When the aperture is under a given head. Mul- 
tiply the area of the aperture, in feet, by the square root 
of the depth, also in feet, and by 5-1 ; the product is the 
quantity discharged, in cubic feet, per second. 

Ex. 1. Required the quantity of water in cubic feet 
per second, discharged through an opening in the side 
of a dam or weir, the width or length of the opening 
being 6k feet, and depth 9 inches, or -75 of a foot 

Square root of -75 = '866. 
„,, 6-5 X -To x -H6G x 5-1 x 2 %A „ nc>n , . ,. 
Then =14-3839 cubic feet. 



Ex. 2. What would be the quantity discharged 
through the above opening, if under a head of water 4 
feet in height ? 

Square root of 4 = 2, and 2 x 5-1 = 10-2 feet, velocity of the 
water per second. And 6-5 x 75 x 2 x 5-1 = 49-725 cubic 
feet discharged in the same time. 

The combined properties of gravity and fluidity which 
water possesses, renders it so available as a source of 
motive power; gravity being the property by which the 
power is produced, and fluidity that by which it is so 
commodiously qualified to the various mollifications in 
which it is employed. 

Water, it is ascertained, is subject to the same laws 
of gravity as those of solid bodies, and thereby accumu- 
lates velocity or effect in an equal ratio when falling 
\hrough an equal space, or descending from an equal 
height. Hence, the velocity attained is as the square 
root of the height of its fall ; and it is xiow quite satis 



PRACTICAL PROPERTIES OF WATER. 85 

factorily decided, that, because of the non-elastic prop- 
erty of water, its greatest is obtained when acting by 
gravity througaout its whole height, whether it be ap- 
plied on a water-wheel, turbine, or other machine 
through which circular motion is to be the immediate 
result. 

In regard to water-wheels, and other machinea 
through which motion is produced by the effort ot 
•water, much discrepancy of opinion has, until lately, 
existed, both as to form and velocity, besides other 
essential points requisite in gaining a maximum of 
effect with the least possible strain ; but these doubts 
are now in a great measure removed through experi- 
ments by the Franklin Institute in this country, added 
to those in France by Morin, and the results of a pa 
tented machine by Whitelaw and Stirrat, Scotland, 
combined with pertinent observations and remarks by 
interested parties in this as well as other countries. 
Hence have been deduced the following demonstrative 
conclusions : — 

1. That, to gain a maximum of effect by a horizontal 
water-wheel, the water must be laid upon the wheel on 
the stream side, and the diameter of the wheel so pro- 
portioned to the height of the fall, that the water may 
may be laid on about 52f degrees distant from the 
summit of the wheel, or the height of the fall, being 1 
the height or diameter of the wheel equal 1-108. 

2. That the periphery of a water-wheel ought to move 
ai; a velocity equal to about twice the square root of the 
fall of the water in feet per second, and the number of 
buckets equal 2-1 times the wheel's diameter in feet; 
also, that precautionary means be adopted for the 
escape of the air out of the buckets, either by making 
the stream of water a few inches narrower than the 
wheel, 4 or otherwise. 

3. That, because of water producing a less efficient 
power by impulse than gravity, turbines, or machines 
through which the motion is obtained by reaction, are 
greatly pnferable to undershot, or low-breast wheels. 



86 PRACTICAL PROPERTIES -OF WATER. 

4. That a head of water is required sufficient to 
cause the velocity of its flowing to be as 3 to 2 of the 
wheel ; i of the wheel's diameter being an approximate 
height, near enough for practical purposes. 

5. That the effective power of a wheel constructed 
according to these restrictions, is equal to the product 
of the number of cubic feet and velocity in feet per 
minute, multiplied into -001325. 



Example for general Illustration. 

Suppose a fall of water 25 feet in height, over which 
is delivered 112 cubic feet per minute; required the 
various peculiar requisites for a wheel *o be in accord- 
ance with the preceding rules. 

1st. 25 x 1-08 = 27 feet, the wheel's diameter. 
2d. V 25 X 2 = 10 feet, velocity of the wheel 
in feet per second. 
Also ; 27 X 2-1 = 56-7, say 57 buckets. 

3d. 27 — 9 = 3 feet, head of water required. 
4th. 112 x 10 X 60 X -001325 = 89 horses' power. 

The turbine of Fourneyron, in France, and the 
patented water-mill of Whitelaw and Stirrat, Scotland, 
have, of late years, attracted a considerable share 
of public attention ; their simplicity of construction 
and asserted effects in like situations, being equal to 
those of the best applied water-wheels. In their manner 
of construction they differ, but in principle they are the 
same ; the action of each being created by a centrifugal 
and tangential force, caused by the weight or impulsion 
of a column of water whose height or altitude is equal 
to twice the height of the fall due to the water's velo- 
city; and in order to produce a maximum of effect in 
cither the one or the other by the pressure and'eentrif- 
ugal force of the effluent water, it is necessary thafthe 
emitting tubes or helical channels of the machine be so 
curved that the apertures shall be in a right line with 
the radius of the wheel. 



STEAM POWER. 



87 



1. That turbines are equally adapted to great as to 

small waterfalls. 

2. That they are capable of transmitting a useful 
effect to from 70 to 78 per cent, of the absolute power. 

3. That their velocities may vary considerably from 
the maximum effect, without differing sensibly from it. 

4. That they will work nearly as effectually when 
drowned to the depth of 6 feet as when free, and, 
consequently, they will make use of the whole of the 
fall when placed below the level of extreme low water. 

5. That they receive variable quantities of water 
without altering the ratio of the power to the effect. 



STEAM POWER. 



There is no application of science to the arts of 
more importance, and more extensive in i{s effects, than 
that of the employment of steam for driving all kinds 
of machinery. It is not my intention to enter into the 
details of the power of steam or the steam-engine, but 
to give some practical rules, the utility of which have 
been tested. 

Steam is of great utility as a productive source of 
motive power; in this respect, its properties are, elastic 
force, expansive force, and reduction by condensation. 
Elastic signifies the whole urgency or power the steam 
is capable of exerting with undiminished effect By 
expansive force is generally understood the amount of 
diminishing effect of the steam on the piston of a 
steam-engine, reckoning from that point of the stroke 
where the steam of uniform elastic force is cut off; but 
it is more properly the force which steam is capable of 
exerting, when expanded to a known number of times 
its original bulk. And condensation, here understood, 
8* 



88 STEAM POWER 

is the abstraction or reduction of heat by another body 
and consequently not properJy a contained property oi 
the steam, but an effect produced by combined agency 
in which steam is the principal; because any coldef 
body will extract the heat and produce condensation, 
but steam cannot be so beneficially replaced by any 
other fluid capable of maintaining equal results. 

The rules formed by experimenters, as corresponding 
with the results of their experiments on the elastic 
force of steam at given temperatures, vary, but ap- 
proximate so closely, that the following rule, because 
of being simple, may, in practice, be taken in preference 
to any other. 

Rule. — To the temperature of the steam, in degrees 
of Fahrenheit, add 100 ; divide the sum by 177 ; and the 
6th power of the quotient equal the force in inches of 
mercury. 

Ex. Required the force of steam .corresponding to a 
temperature of 312°. 

312+100 

= 2-3277° = 159 inches of mercury. 

17« 3 

To estimate the amount of advantage gained by using 
steam exjiansively in a steam-engine. 

When steam of a uniform elastic force is employed 
throughout the whole ascent or descent of the piston, 
the amount of effect produced is as the quantity of 
steam expended. But let the steam be shut off at any 
portion of the stroke, — say, for instance, at one-half, — 
it expands by degrees until the termination of the 
stroke, and then exerts half its original force ; hence 
an accumulation of effect in proportion to the quantity 
of steam, 

Rule. — Divide the length of the stroke by the dis- 
tance or space into which the dense steam is admitted, 
and find the hyperbolic logarithm ot the quotient, to 
which add 1 ; ,ind the sum is the ratio of the gain. 



STEAM POWER. Si> 

Ex. Suppose an engine with a stroke of 6 feet, and 
»ne steam cut off when the piston has moved through 
; required the ratio of gain by uniform and expansive 
force. 

<;-^2 = 3; hyperbolic logarithm of 3= 1-0986 + 1 =2-0986, 
ratio of effect 5 that is, supposing the whole effect of the 
steam to be 3, the effect by the steam being cut oft at 
£ = 2-0986. 

Again ; let the greatest elastic force of steam in the 
cylinder of an engine equal 48 lbs. per square inch, 
and let it be cut off from entering the cylinder when 
the piston has moved 4^ inches, the whole stroke being 
18 ; required an equivalent force of the steam through- 
out the whole stroke. 

18 — 4-5 = 4, and 48 — 4= 12. 

Logarithm of 4+ 1 =2-38629. 

Then 2-38629 X 12 = 28-635 lbs. per square inch. 

In regard to the other case of expansion, when the 
temperature is constant, the bulk is inversely as the 
pressure; thus, suppose steam at 30 lbs. per square 
inch, required its bulk to that of original bulk, when 
expanded so as to retain a pressure equal to that of the 
atmosphere, or 15 lbs. 



15 + 30 
15 



= 3 times its original bulk. 



It is because of the latent heat in steam, or water m 
an aeriform state, that it becomes of such essential 
service in heating, boiling, drying, &c. In the heating 
of buildings, its economy, efficiency, and simplicity of 
application, are alike acknowledged ; the steam, being 
simply conducted through all the departments by pipes, 
by extent of circulation condenses, — the latent heat 
being thus given to the pipes, and diffused by radiatirn. 
In boiling, its efficiency is considerably increased, if 
advantage be taken of sufficiently enclosing the fluid, 
and reducing the pressure on its surface, by means of 



90 PRODUCTION OF STEAM. 

an air-pump. Thus, water in a vacuum boils at about 
a temperature of ys°; and in sugar-refining, where 
such means are employed, the sirup is boiled at 150 = 

Effects produced by Water in an Piriform State. 

When water in a vessel is subjected to the action of 
fire, it readily imbibes the heat, or fluid principle of 
which the fire is the immediate cause, and, sooner or 
later, according to the intensity of the heat, attains a 
temperature of 212° Fahrenheit. If, at this point of 
temperature, the water be not enclosed, but exposed to 
atmospheric pressure, ebullition will take place, and 
steam or vapor will ascend through the water, carrying 
with it the superabundant heat, or that which the water 
cannot, under such circumstances of pressure, absorb, 
to be retained, and to indicate a higher temperature. 

Water, in attaining the aeriform state, is thus uni- 
formly confined to the same laws, under every degree 
of pressure ; but, as the pressure is augmented, so is 
the indicated temperature proportionately elevated 
Hence the various densities of steam, and correspond- 
ing degrees of elastic force. 



PROPERTIES OF STEAM. 



91 



Table of the Elastic Force of Steam, and corresponding 
Temperature of the Water with which it is in Contact. 



Pressure per 


Elastic Force in 


Temperature in Decrees of 


Volun.e 


(square inch, 

atmospheric 

pressure 

include*!. 








of Steam 
compared 
with Vol. 
of Water. 


Inches of 
Mercury. 


Mares of 
Mercury. 


Fahr. 


Reaum. 


Cent. 


lbs. 

14-7 


kilos*. 

6-668 


30-00 


•762 


2120 


800 


1000 


1711 


15 


6-80 


30-60 


•778 


212-8 


80-4 


100-4 


1670 


16 


7-26 


32-64 


•829 


216-3 


81-9 


102-4 


1573 


17 


7-71 


31-68 


•880 


219-6 


83-3 


104-2 


1488 


18 


8-16 


36-72 


■932 


222-7 


84-7 


105-9 


1411 


19 


8-62 


38-76 


•984 


225-6 


86 


107-6 


1343 


20 


907 


40-80 


J -037 


228-5 


87-3 


109-2 


1281 


21 


9-52 


42-84 


1-089 


231-2 


88-5 


110-7 


1225 


22 


9-98 


44-88 


1-140 


233-8 


89-7 


1121 


1174 


23 


10-43 


46-92 


1-192 


236-3 


908 


113-5 


1127 


24 


10-88 


48-96 


1-244 


238-7 


91-9 


114-8 


1084 


25 


11-34 


51-00 


1-296 


241-0 


930 


1161 


1044 


26 


11-79 


53.04 


1-318 


243-3 


93-9 


117-4 


1007 


27 


12-25 


5503 


1400 


245-5 


94-9 


118-6 


973 


28 


12-70 


57-12 


1-452 


247-6 


95-8 


119-3 


941 


29 


1315 


59-16 


1-503 


249-6 


96-7 


120-9 


911 


30 


13-61 


61-21 


1-555 


251-6 


97-6 


122-0 


883 


31 


14-06 


63-24 


1-607 


253-6 


98-5 


1231 


857 ' 


°u 


1451 


65-23 


1659 


2doo 


99-3 


124-2 


833 ) 


33 


14-97 


67-32 


1-711 


257-3 


1001 


125-2 


810 


34 


15-42 


69-36 


1-763 


259-1 


100-9 


126-2 


788 


35 


15-87 


71-40 


1-814 


260-9 


101-7 


127-2 


767 


36 


16-33 


73-44 


1-866 


262-6 


102-5 


128-1 


748 


37 


16-78 


75-48 


1918 


264-3 


103-2 


129-1 


729 


38 


17-23 


77-52 


1-970 


265-9 


104-0 


129-9 


712 


39 


17-69 


79-56 


2-022 


267-5 


104-7 


130-8 


695 


40 


18-14 


81-60 


2-074 


269-1 


105-4 


131-7 


679 


41 


18-59 


83-64 


2-] 26 


270-6 


106-0 


132-6 


664 


42 


1905 


85-68 


2-178 


272-1 


106-7 


133-4 


649 


43' 


19-50 


87-72 


i-229 


273-6 


107-4 


131-2 


635 


44 


19-96 


89-76 


2-281 


2750 


108-0 


135-0 


622 


45 


20-41 


91-80 


2-333 


276-4 


108-6 


135-8 


610 


46 


20-86 


93-84 


2-385 


277-8 


109-2 


136-6 


598 


47 


21-32 


95-83 


2-437 


279-2 


109-9 


137-3 


586 


48 


21-77 


97 r »2 


2-489 


280-5 


110-4 


138-1 


575 


49 


22-22 


99-b6 


2-541 


281-9 


1111 


138-8 


564 


50 


22-68 


102-00 


2-592 


283-2 


11 If 


1396 


554 



92 PROrLRTIES OF STEAM. 

The preceding table is peculiarly adapted for esti 
mating the power of steam engines on the condensing 
principle, because, in such, the effective force of the 
Bteam is the difference between the total force and the 
resisting vapor retained in the condenser. The fol- 
lowing table is more adapted for estimating the effects 
of non-condensing engines ; as, in such, the atmos- 
pheric pressure is not generally taken into account, 
engines of this principle being supposed to work in a 
medium; or, the atmospheric pressure on the boilers, 
to cause a greater density of steam, is equal to the 
resisting atmosphere which the effluent steam has to 
contend with, on leaving the cylinder. 

Steam, independent of the "heat indicated by an im- 
mersed thermometer, also contains heat that cannot be 
measured by any instrument at present known, and, in 
consequence of which, is termed latent or concealed 
heat ; the only positive proof we have of its existence 
being that of incontestable results, or effects produced 
on various bodies. Thus, if one part, by weight of 
steam at 212°, be mixed with nine parts of water at 
62°, the result is water at 178-0° ; therefore, each of the 
9 parts of water has received from the steam 116-6° of 
heat, and consequently, the steam has diffused, or given 
out, 116-6 X 9 = 1049-4 — 33-4 = 1016° of heat, which 
it must have contained. 

Again ; it is ascertained, by experiment, that if one 
gallon of water be transformed into steam at 212°, and 
that allowed to mix with water at 52°, the whole will be 
raised to the boiling point, or 212°. From these and other 
experiments, k is ascertained that the latent heat in 
steam varies from 940° to 1044°, the ratio of accumula- 
tion advancing from 2J2°, as the steam becomes more 
dense and of greater elastic force. Hence, the severity 
of a scald by steam to that of boiling water. 

Water holding impurities in solution tends to retard 
its attaining the aeriform state, and so impairs the 
amount of its elastic force at an equal temperature, a* 



PROPERTIES OF STEAM. 



93 



exhibited in the following tables. Thus, commoD 
water boils at 212° Fahrenheit. 



Name of substance. 


Proportionate quantity in 

100 parts 

by weight of water. 


Boiling 
points. 


Sails in sea water. 


3-03. 


213-2° F. 


Sulphate of soda 

Sulphate of iron 


<o 

C 

a 
S 
£ 

o 

c 


31-5 
64 

52 

45 

57-5 

30 

60 

60 


213 
216 

220 
220 
222 
22*4 
246 
256 


Sulphate of lime 

Sulphate of magnesia . . 

Muriate of soda 

Nitrate of soda 

Acetate of soda 



Elastic Force of Steam in Inches of Mercury. 

Common water ) boiling point, 212° F. ( elastic force, 30 in 
Sea water . . . $ at 212 " } " 23-05 « 

Common water £ boiling point, 21G° F. ( elastic force, 32-5 in. 
Sea water. . . \ at 216 « { " 24-6 " 

Common water ) boiling point, 220° F. ( elasti* force, 35-1 in. 
Sea water ... $ at 220 " { " 26-5 « 

Hence the propriety of procuring, for steam, water m 
its purest state. 

Effects produced by Air in its natural and also in a 
rarefied State. 

The weight or pressure of the atmosphere is equal to 
the weight of a column of water 34 feet in height, or to 
a column of mercury 30 inches in height, or to 14-7 lbs. 
average per square inch, at a mean temperature. But 
air, like all other gases, is rendered lighter by the ap- 
plication of heat; for then the particles of the mass are 
repelled from each other, or rarefied, and occupy a 
greater space. Rarefied air, being specifically lightest, 
mounts above that of common density ; hence change 
of temperature, and the principal cause of winds. 



/ 

94 PROPERTIES OF All*. 

liable of the Expansion of atmospheric Air by Heat. 




Degrees of 
j Fahrenheit. 


Balk. 


| Degrees of 
Fahrenheit. 


Bulk. 


Degrees of 
Fahrenheit. 


Bulk. 




j 32° 
1 35 
40 
I 45 
I 50 
1 55 
| 60 


1000 
1007 
1021 
1032 
1043 
1055 
1Q66 


65° 

70 

75 

80 
85 
90 
95 


1077 
1089 
1099 
1110 
1121 
1132 
1142 


100° 

120 

140 

160 

W0 

200 

212 


1152 
1194 
1235 
1275 
1315 
1364 
1376 


The pressure or gravity of the atmosphere, being 
equal to a column of water 34 feet in height, is the 
means or principle on which rests the utility of the 
common pump, also of the syphon and all other such 
hydraulic applications. In a pump, the internal pres- 
sure on the surface of the liquid is removed by the 
tction of the bucket ; and as by degrees the density 
becomes lessened, so the water rises by the external 
pressure to the above-named height; and at such 
• height it will remain, un3ess, by some derangement of 
construction taking place, the atmospheric fluid is 
allowed to enter and displace the liquid column. But 
observe, if the temperature of the water or other liquid 
be so elevated that steam or vapor arise through it, 
ishen according to the vapcr's accumulation of density 
may the action of the pump be partially or wholly 
destroyed ; and the on] y ineoijs >f evasion in such cases 
fs, to plac*; the working buck?! beneath the surface of 
\he Ii^utu which s requWi '< *)e raised. 



/ ' ' -s 

pumps. 95 


Table showiiig the Quantity of Water per Lineal Foot in 




Pumps, or Vertical Pipes of different Diameters. 






Diameter 


Numberof 


Numberof 


Diameter Numberof Numberof 






of pump 


gallons per 


cubic feet 


of pump 


gallons per 


cubic feet 






in inches. 


lineal ft. 


per tin. ft. 


in inches. 


lineal ft. 


per lin ft. 




2 


136 


•02 i 8 


8 


2176 


•3490 




2 X 


•172 


•0276 


8i 


2 314 


•3712 






3 


•212 


•0340 


84 


2-456 


■3!U0 






21 


•257 


•0412 


81 


2-603 


•4175 






3 


•306 


•0490 


9 


2-754 


•4117 






H 


•359 


•0576 


n 


2-90!) 


•4666 






3| 


•416 


•0668 


94 


3-068 


•4923 






31 


■478 


•0766 


01 


3-232 


•5184 






4 


•544 


•0872 


10 


3-400 


•5454 






4k 


•614 


•0985 


m 


3-572 


5730 






44 


•688 


•1104 


104 


3-748 


•6013 






41 


•767 


•1230 


101 


3-929 


•6302 






5 


•850 


•1363 


n 


4-114 


•6599 






H 


•937 


•1503 


Hi 


4-303 


6902 






54 


1-028 


•1649 


H4 


4-496 


•7212 






51 


1 124 


•1803 


ill 


4-694 


•7529 






6 


1224 


•1963 


12 


4-896 


•7853 






6| 


1-328 


•2130 


124 


5-312 


•8521 






64 


1-436 


•2304 


13 


5 746 


•9217 






61 


1-549 


•2489 


134 


6 196 


•9939 






7 


1-666 


•2672 


14 


6 664 


1-0689 






H 


1-787 


•2866 


15 


7 650 


1 2271 






74 


1-912 


•3067 


16 


8-704 


1-3962 






n 


2-042 


•3275 1 


18 


11-016 


1-7670 






Examples illustrative of the Utility of the ' 


Fable. 


I. Required the quantity of water lifted by each 


stroke of the bucket of a 94 -inch pump, the length of 


the stroke being 2£ feet. 


3-06S x 2-25=6-903 gallons, each stroke. 


2. What length of stroke with a 6-inch pump will 


ve necessary, to discharge 44 gallons of watei pel 
9 



96 PROPERTIES OF AIR. 

minute, the number of strokes being 18 m the given 
time? 

44 

= 2 feet, the length of stroke. 

1-224 x 18 

3. What must be the diameter capable of raising 
25 cubic feet of water per minute, the length of the 
stroke being 2£ feet, and making 1(3 effective strokes 
per minute ? 

25 

= -625, or 103 inches, nearly. 

2-5 x 16 4 

It is by the oxygen of the atmosphere that com- 
bustion is supported. The common combustibles of 
nature are chiefly compounds of carbon and hydrogen, 
which, during combustion, combine with the oxygen 
of the atmosphere, and are converted into carbonic 
acid and watery vapor, different species of fuel re- 
quiring different quantities of oxygen. The quantity 
required for the combustion of a pound of coal varies 
from 2 to 3 lbs., according to the quality of the coal. 
60 cubic feet of atmospheric air is necessary, to pro- 
duce 1 lb. of oxygen. 

The pressure or fluid properties of the atmosphere 
oppose bodies in passing through it, the opposing re- 
sistance increasing as the square of the velocity of the 
body, and the resistance per square foot in lbs. as its 
velocity in feet per second, multiplied into -002288. 
Thus, suppose a locomotive engine in a still atmosphere, 
at a velocity of 25 miles per hour, presents a resisting 
frontage of 20 feet; required the amount of opposing 
resistance at that velocity. 

25 miles per hour equal 3667 feet per second. 
Then 36-672 x -002288 x 20 = 61-5 i^ constant opposing 
force 



WINDS. 



9*5 



Table of the Force and common ^Appellations given U 
Winds at different Velocities. 



Velocity of the Wind in 



Feet per 
second. 



Miles per 
hour. 



1 
2 

3 
4 
5 
10 
15 
20 
25 
30 
35 
40 
45 
50 
60 
80 



Force in lbs.; 

avoirdupois I Common Appellation? 
per square given to the Wind. 

foot. 



147 


•005 


2-93 


•020 


440 


•044 


5 87 


•079 


733 


123 


14-67 


•492 


22-00 


1 107 


29-34 


1 968 


36 67 


3075 


4401 


4-429 


51-34 


6 027 


58-68 


7-873 


66 01 


9-963 


73 35 


12-300 


8802 


17 715 


117-36 


31-490 



Hardly perceptible. 
Just perceptible. 

Gentle, pleasant wind 

Pleasant, brisk gale. 

Very brisk. 

High winds. 

Very high. 

A storm or tempest. 
A great storm. 
A hurricane. 



In order to gain the greatest amount of the wind's 
impulsive effect, to produce rotary or circular motion by 
the sails of a wind- mill, the total surface of the saila 
presented to the wind ought to be about seven-eighths 
of the circle's surface which is formed by their motion, 
and each sail angled to the plane of motion as follows, 
the whip or back being divided into six equal parts: — 

Distance from centre of motion, 1 2 3 4 5 6 ) Smeato '• 
■ nple with plane of motion, 18° 19 18 16 12$ 7 \ rule 
■iy G. Forrester, Liverpool, 24° 21 18 H 9 3 



98 FRICTION. 



FRICTION. 



Friction is an effect produced by bodies nibbing 
one upon another, which acts as a retarding influence 
in the motion of all mechanical contrivances, hut 
might not unfrequently be considerably diminished by 
a due regard to its iaws, and a proper attention to 
the selection of those materials on which a uniform 
smooth surface may he attained, and which, according 
to experiments, are least liable to tear or become hot, 
and cause a roughness to arise when in working 
contact. 

Several doubts existed, until lately, respecting the 
laws of friction ; but those are now entirely removed, 
through the experiments of Mr. G. Rennie, on his own 
account, and those of M. Morin, acting for, and under 
the sanction of, the French government, from or by 
which the -following laws have been fully established : — 

1. The friction accompanying the motion of two 
surfaces, between which no unguent is interposed, 
bears the same proportion to the force by which those 
surfaces are pressed together, whatever may be the 
amount of that force. 

2. This friction is independent of the extent of the 
surfaces of contact. 

3. Where unguents are interposed, a distinction is 
to be made between the case in which the surfaces are 
simply unctuous and in intimate contact with one 
another, and the case in which the surfaces are wholly 
separated from one another by an interposed stratum 
of the unguent. If the pressure upon a surface of 
contact of given dimensions be increased beyond a 
certain limit, the latter of these cases passes into the 
first; the stratum of unguent being pressed out, and 
the unctuous , surfaces, which it separated from one 



FRICTION. 99 

mother, being- brought into intimate contact. As long 
as either of these two states remain, the laws of its 
friction are not affected by the presence of the unguent, 
but, in the transition from the one state to the other, an 
exception is made to the independence of the friction 
upon the extent of the surface of contact ; for. sup- 
posing the extent of two surfaces of contact, between 
which a stratum of unguent is interposed, and which 
sustain a given pressure, to be continually diminished, 
it is. evident, that the portions of this pressure which 
take effect upon each element of the surfaces of con- 
tact will be continually increased, and that they may 
thus be so increased as to press out the interposed 
stratum of unguent, and cause the state of the surfaces 
to pass into that which is designated as unctuous, 
thereby changing the coefficient of friction. That 
law of friction, then, which is known as the law of : : 
the independence of the surface, is to be received, in 
the case where a stratum of unguents is interposed, 
only within certain limits. 

It will be understood, from what has been said, that 
there are three states, in respect to friction, into which 
the surfaces of bodies in contact may be made suc- 
cessively to pass : one, a state in which no unguent is 
present; the second, a state in which the surfaces are 
unctuous, but intimately m contact; the third, a state 
in which the surfaces are separated by an entire 
stratum of the interposed unguent. 

Throughout each of these states, the coefficient ot 
friction is the same; but it is essentially different in 
the different states. 

4. It is a law common to the friction of all the 
states of contact of two surfaces, that their friction, 
when in motion, is altogether independent of the 
velocity of the motion. M Morin has verified this 
law, as well in various stites of contact without inter- 
Dosed fluids, as in the cases where, water, oils, grease, 
glutinous liquids, sirups, pitch, were interposed in a 
continuous stratum. 

9# t 



100 BOILERS. 

The variety of the circumstances under which these 
laws obtain in respect to the friction of motion, and 
the accuracy with which the phenomena of motion 
accord with them, may be judged of from one example, 
taken from the first set of experiments of M. Monn 
upon the friction of surfaces of oak, whose fibres were 
parallel to the direction of their motion upon one 
another. He caused the surfaces of contact to vary 
their dimensions in the ratio of 1 to 84, — from less 
than 5 square inches to nearly 3 feet square;* the 
forces Avhich pressed them together he varied from 
88 lbs. to 2205 lbs., and their velocities from the slow- 
est possible to 9-8 feet per second, — causing them to 
be at one period accelerated motions, at another uni- 
form, at a third retarded; yet, through all this wide 
range of variation, he in no instance found the co- 
efficient of friction to deviate from the same fraction 
of 0-478 by more than ^ of the amount of the 
fraction. 



RULES, TABLES, ETC., RELATIVE TO 
BOILERS AND THE STEAM-ENGINE. 

The boiler of a steam-engine may be explained as 
that portion of the structure in which the vital prin- 
ciple of the engine is generated ; consequently, its 
construction is of the utmost importance ; for upon the 
proper efficiency of the boiler depends, in a great 
measure, the efficiency of the engine. 

Boilers not unfrequently, because of unavoidable 
peculiarities, are necessarily constructed of various 
forms ; but, for land or stationary engine boilers, if no 
thwarting circumstances intervene, either the wagon 
or cylindrical forms are commonl} resorted to; the 



BOILERS J01 

former for those of condensing engines, and the lattel 
for those of the high-pressure principle. 

In the construction of boilers, much attention ought 
to be paid in avoiding thin films of water where the 
action of the fire is great ; because it is neither con- 
sistent with safety, nor can there be the proper quan- 
tities of steam generated, according to the surface 
exposed, unless under some extraordinary degree of 
pressure. Also, convex surfaces, exposed to the actior. 
of the steam, unless properly supported, ought strenu- 
ously to be avoided. Large water spaces, concave 
surfaces, or straight plates securely stayed, with ample 
steam-room, are the chief requisites to U-° attended to. 

1. To determine the proper quantity of heating sur- 
face in a boiler for an engine with a cylinder of a given 
capacity, and, steam at any density required. 

Rule. — Multiply 375 times the area of the cylinder 
in feet by the velocity of the piston in feet per minute, 
and divide the product by the volume of steam to 1 of 
water at the density required, (see Table, page 91 ;) 
and the quotient is the amount of effective heating 
surface in square feet. 

Ex. Required the amount of effective heating sur- 
face in a boiler for an engine whose cylinder is 4£ 
square feet in area, and the piston's velocity 224 feet 
per minute, the pressure of the steam to equal 5 lbs. 
per square inch above the pressure of the atmosphere. 

375 x 4-5 x 224 

=295 square feet, nearly ; the fire-prate be- 

1282 ■ J h 

ing in accordance with the following rule. 

Multiply the number of square feet of heating sur- 
face by 43J the product equal the area of fire-grate in 
square feet, thus : — 

295 x 12 = 35-4 square feet of furnace bar. 

Note. — By effective heating surface is meant horizontal sur- 
faces over tire, flame, or heated air; vertical or side surface! 
requiring about 1$ foet to equal in effrct ' of horizontal su**a< » 



02 BOILERS. 

2. To determine the proper dimensions for a wagon- 
»haped boiler, when the amount of effective heating sur* 
face in square feet is obtained by the preceding ride. 

1. The bottom surface equal half the whole surface 

2. The length of the boiler equal twice the square 
root of bottom surface. 

3. The width equal one-fourth the length; and 

4. The height equal one-third the length. 

Ex. Required the dimensions for a boiler of the 
wagon form, that may present an effective heating sur- 
face of 295 square feet 

Bottom surface =295 — 2, or 147-5 square feet 
Length . . . = V147-5 x 2, or 24-26 feet. 
Width . . . = 24-26 — 4, or 6-06 feet. 
Height. . . =24-26-|-3 r or 808 feet. 

Note. — The amount of side or vertical surface equal twice 
the length of the boiler, added to the width, and multiplied by 
•75 to obtain that of effective surface } hence, 

147-5 x 175 

= 4-7 feet, depth of side flue. 

24-26 X 2 4- 6-06 

3. To determine the dimensions for a cylindriccu 
boiler. 

Rule. — Extract the square root of 1-34 times the 
effective heating surface in square feet, and twice the 
root equal the boiler's circumference in feet; also, the 
circumference equal the length. 

Ex. Let a cylindrical boiler be required with ai 
effective heating surface of 8(i square feet; what mus 
be its lensfth and diameter in feet? 



V86 X 1-34= 10-74 x 2 = 21-48 feet circumference, or b 
feet 10 inches diameter, and 21-48 feet in length. 

Note. — When an internal flue is to be inserted in a boilei 
be external surface of the boiler may be diminished in length 



I 1 



BOILERS 



I0SN 



equal to half the exposed surface of the flue Observe, also, 
that the height of the contained water in boilers generally 
ought to be about two-thirds the whole height of the boiler 



Specified Particulars relative to the Boiler and Engine. 

Diameter of cylinders, . 14 inches. 

Length of stroke, 18 " 

Lap of the valve, 1 inch. 

Diameter of driving wheels, 5^ feet. 

Length of internal fire-box, . . . 2 feet ll| inches. 

Width of do. 3 " 5 

Length of cylindrical part of boiler, 8 " 8 a 

Diameter of do., 3 " 4A " 

Length of tubes, 8 " 11$ " 

JMumber of tubes, 133, of brass. 

Interior diameter of do., 1| inches. 

Diameter of blast-pipe, 4 " 

About 312 lbs. of coke, consumed in this boiler 
evaporate 84 gallons of water ; and from 20 to 25 lbs 
of coke are consumed per mile. 



Heating Powers of Combustible Substances 



Species of combustible. 


lbs. of 
water 
heated 
from 32° 
to 212°. 


lbs. of boil- 
ing water 
evaporated 
by 1 lb. of 
fuel. 


lbs. of 
atmospheric 
air to each 
lb. of fuel. 


Wood in its ordinary state 

Wood charcoal 

Coal 


26 
73 
60 
65 
30 
64 


4-72 
13-37 
10-90 
11-81 

5-45 
11-63 


4-47 
11-46 

9 26 




11-46 j 


Turf 

Tu-f charcoal 


460 
9-86 



104 



STEAM -ENGINES. 



Table of Dimensions for Steam-Engine Cylinders by 
celebrated Makers. 



St.itionnry Con- 

dciiMng Engines, 

by L'oukon & Watt. 






81 

18 
194 
21 



23| 

244 

26 

27 

27^ 

28 

29 

30 

324 

344 

38| 

424 



Marine Engines, 
by Mruulsley, 
Nupier, &e. 



10 
IS 

20 

25 

30 

40 

.50 

60 

70 

80 

90 

100 

110 

120 

130 

1.30 

200 

250 



£ S - 


°J 


"5 * 


III 


& e 


1* 


■5 o"— 


■33 


if 


O 




■ 




20 


2 


1 


24 


2j 


2 


27 


25 


3 


29J 


4 


32 


3 


5 


36 


3.A 


6 


40 


4 


7 


43 


4 


8 


464 


44 


9 


4% 


44 


10 


60 


4$ 


11 


53 


5 


12 


554 


54 


14 


57 


54 


16 


60jj 


fii 


18 


65 


6 


20 


74^ 


6 


25 


84 


b 


30 



High-Pressure, or 

Non-Comiensing Engine*, 

bv various .-hake re. 



Diameter* of cylinders, 

the force of the steam being, 

per square inch, 



lbs. 40 lbs. 50 lbs 



The unit of nominal power for steam-engines, or the 
usual estimate of dynamical effect per minute of a 
horse, called, by engineers, a horse-power, is 33,000 lbs., 
at a velocity of 1 foot per minute ; or, the effect of a 
load of 200 lbs., raised by a horse, for 8 hours a day, 
at the rate of 24 miles per hour, or 150 lbs. at t'.e rate 
of 220 feet per minute 



TROPKHTILS OF BODIES. 



10-; 



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-op ui nuiad Sur.iaj^ 



•^ C! M CO C3 
_ I n t- r- O I 



2^2 ' S ' g I I I 



•A\iAvt2 oyioads 



r- *• r- r^ £• 1- 



2 % 



.5 £ p-o «B g a. 

S_ C ^. - =. ~ o 



I 3 



c c 





i 
106 PROPERTIES OF BODIES. 




WOODS 






sf 


ojg 


c 


i 6 S • 


Comparative 




Names. 


2 o 




*! 

o 

s 


Ultimate co 

aive strengtl 

an inch sqi 

prism in lb 


09 
| 


a 
a 


i 

a 

'3> 




English oak 


934 


58 


3^ 


11880 


100 


100 


100 




Riga do 


872 


54 


12888 


93 


108 


125 






Dantzic do 


756 


47 


48 


12780 


117 


107 


99 






American do 


672 


42 


53 


10253 


114 


86 


64 






Beech 


852 


48 


45 


12225 


77 


103 


138 






Alder 


BOO 


4tf 


484 
55" 


9540 


63 


80 


101 






Plane 


640 


40 


10935 


78 


99 


108 






Sycamore 

Chestnut 


604 


38 


59 


9630 


59 


81 


111 






610 


38 


59 


10656 


67 


89 


118 






Ash 


845 


52 


43 


1413a 


89 


119 


160 






Kim 


673 


42 


53 


9720 


78 


82 


86 






Mahogany, Spanish . 
" Honduras 


800 


50 


45 


7560 


73 


67 


61 






637 


40 


55 


11475 


93 


96 


99 






Walnut 


671 


42 


53 


8800 


49 


74 


111 






Teak 


750 


46 


48* 


12915 


126 


im 


94 






Poona ......... 


640 


40 


55 


12350 


99 


82 






African oak 


944 


59 


38 


17200 


101 


138 






Poplar 


383 


34 


66 


5928 


4* 


CK> 


57 






Cedar 


561 


33 68 


7420 


28 


62 


106 






Riga fir 


753 


47 


48 


9540 


98 


80 


6t 








546 


34 

33 


66 
63 


9540 
7110 


114 
55 


80 

60 


56 
65 




Scotch do 


528 




Christ. VVht. deal . . . 


590 


37 


60 


12346 


104 


104 


104 






Amer". white spruce . 


551 


34 


66 


10296 


72 


86 


102 






Yellow pine 


461 


28 


80 


11853 


95 


99 


103 






Pitch pine 


660 


41 


54* 


9796 


73 


82 


92 






Larch 


530 


31 


72 


12240 


79 


103 


134 






Cork 


240 


15 


149 


— 


— 

















PROPERTIED OF BOD ES. 



1U7 



LIQUIDS. 


GA3E3. 




>; 


„ c 


Atmospheric air being the 




>§' 


S~ 


standard of comparison, 


Names. 


is 


-Cra~ 


or 1000. 




o • 




<c * 


.2f ■'= .£ 




<e m* 




i* 


si 


Names. 


il 




cc 






91 Si 


Acid, sulphuric 


1850 


18-5 


Hydriodic acid gas 


4340 


" nitric . . 


1271 


12-7 


Chlorine " " 


2500 


" muriatic . 


1200 


12-0 


Carbonic " " 


1527 


** fluoric . 


106C 


10-6 


.Nitrous oxide " 


1527 


" citric . 


1034 


10-3 


Cyanogen a 


1805 


" acetic . . 


1062 


106 


Oxygen u 


1111 


Water from the 






Carbonic oxide " 


972 


Baltic 


1015 


10-2 


Carbureted hy- 




Water from the 






drogen " 


972 


Dead Sea . . . 


1240 


12-4 


Prussic acid " 


937 


Water from the 






Ammoniacal u 


590 


Mediterranean 


1029 


10-3 


Steam of water " 


623 


Water, distilled 

Oils, expressed : 

linseed .... 


1000 


100 


Hydrogen " 


69 


940 


9-4 


Weight of water at the 


sw\,t almond 


932 


9-3 


common temperature : 


w! .le .... 


923 


9-2 


1 cubic in. = -03617 lb. 


hempseed . . 


926 


9-3 


1 " ft. =r 62-5 lbs. i 


olive 

Oils, essential ; 


915 


9-2 


1 " " = 6-25 imp. galls 
1-8 " " = 1 cwt. 

Icylin. in.= -028451b. 


cinnamon . . 


1043 


10-4 


1 " ft. —49-1 lbs. 


lavender . . . 


894 


8-9 


1 " " = 5 imp. galls. 


turpentine . . 


870 


8-7 


2-282 feet = 1 cwt. 


amher .... 


868 


8-7 


11-2 imp. galls. = 1 cwt. 


Alcohol 


825 


8-2 


224 " " = 1 ton. 


Ether, nitric . . 


908 


91 




Proof spirit . . 


922 


9-2 


1 


Vinegar 


1009 


101 


_J 



10 



PRACTICAL TABLES. 109 



PRACTICAL TABLES. 



WEIGHT OF METALS. 



WROUGHT IRON J SQUARE, ROUND, AND FLAT 

Table I. contains the weight of Square Iron in sizes, 
from | inch to six inches square, advancing by $ inch 
and from 6 to 12 inches square, advancing by | inch ; 
and in lengths, from 1 foot to 18 feet. The sizes are 
arranged in the first column of each page, and the 
lengths along the top ; the weight in lbs. immediately 
under the lengths, and in a line with the sizes. 

Table II. contains the weight of Round Iron in sizes 
from \ inch to 6 inches diameter, advancing by \ inch ; 
and from 6 to 12 inches diameter, advancing by \ inch ; 
and in lengths from 1 foot to 18 feet The sizes, 
lengths, and weights are arranged as in Table I. 

Table III. contains the weight of Flat Iron in 
widths, from £ inch to 6 inches diameter, advancing by 
| inch ; in thicknesses from | inch to 1 inch, advancing 
by \ inch; and in lengths, from 1 to 18 feet The 
widths, lengths, and weights, are arranged as in the 
preceding tables, and the thicknesses alongside of tUa 
widtha 



110 






PRACTICAL TABLES. 
















TABLE I 


.-SQUARE IRON. 












size. 


1ft. 


2 ft. 


3ft. 


4ft. 


5 ft. 


6 ft. 


7ft. 


8 ft. 


9ft. 






inch. 


bs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


it* 






4 


0-2 


04 


0-6 


0-8 


1-1 


13 


1-5 


1-7 


19 








1 


0-5 


10 


14 


1-9 


2-4 


2-9 


3-3 


3-8 


4-3; 






h 


0-8 


17 


2-5 


3-4 


4-2 


5-1 


5-9 


6-8 


7-6 








§ 


1-3 


2-6 


4-0 


5-3 


6-6 


7-9 


9-2 


10-6 


11-9 








i 


1-9 


3-8 


5-7 


7-6 


9-5 


11-4 


13-3 


15-2 


17-1 








l 


2-6 


5-2 


7-8 


10-4 


12-9 


15-5 


18-1 


20-7 


23-3 










3-4 


6-8 


10-1 


13-5 


16-9 


20-3 


23-7 


27-0 


30-4 








li 


4-3 


8-6 


12-8 


171 


21-4 


25-7 


29-9 


34-2 


38-5 








U 


5-3 


10-6 


15-8 


21-1 


26-4 


31-7 


37-0 


42-2 


47-5 








11 


6-4 


12-8 


19-2 


25-6 


32-0 


38-3 


44-7 


51-1 


57-5 








u 


7-6 


15-2 


22-8 


30-4 


38-0 


45-6 


53-2 


60-8 


68-4 








1§ 


8-9 


17-9 


26-8 


35-7 


44-6 


53-6 


62-5 


71-4 


80-3 








11 


10-4 


20-7 


31-1 


41-4 


51-8 


621 


72-5 


82-8 


93-2 








li 


11-9 


23-8 


35-6 


47-5 


59-4 


71-3 


83-2 


95-1 


106-9 








2 


13-5 


27-0 


40-6 


54-1 


67-6 


8M 


94-6 


108-2 


121-7 








2* 


15-3 


30-5 


45*8 


61-1 


76-3 


91-6 


106-8 


122-1 


137-4 








2* 


17 1 


34-2 


51-3 


68-4 


85-6 


102-7 


119-8 


136-9 


154-0 








2| 


19-1 


38-1 


57-2 


76-3 


95-3 


114-4 


133-5 


152-5 


171-6 








2i 


21-1 


42-2 


63-4 


84-5 


105-6 


126-7 


147-8 


169-0 


190-1 








2| 


23-3 


46-6 


69-9 


93-2 


116-5 


139-8 


163-0 


186-3 


209-6 








2| 


25-6 


51-1 


76 7 


102-2 


127-8 


153-4 


178-9 


204-5 


230-0 








2J 


27-9 


55-9 


83-8 


111-8 


139-7 


167 6 


195-7 


223-5 


251-5 








3 


30-4 


60-8 


91-2 


121-7 


152-1 


182-5 


212-9 


243-3 


273-7 








3S 


33-0 


66-0 


99-0 


132-0 


165-1 


198-1 


231-1 


264-1 


297-1 




i 




34 


35-7 


71-4 


107-1 


142*8 


178-5 


214-2 


249-9 


285-6 


321-3 








31 


38-5 


77-0 


115-5 


154-0 


192-5 


231-0 


269-5 


308-0 


346-5 








3d 


41-4 


82-8 


124-2 


165-6 


207-0 


248-4 


289-8 


331-3 


372-7 








3| 


44-4 


88-8 


133-3 


17--7 


222-1 


266-5 


310-9 


355-3 


399-8 








3:1 


47-5 


95-1 


142-r. 


190-1 


237 7 


285-2 


332 7 


380-3 


427-8 








3g 


50-8 


101-5 


152-3 


203-0 


253-8 


304-5 


355-3 


406-0 


456-8 



































PRACTICAL TABLES. Ill 






TABLE I. -SQUARE IRON. 






size. 


10ft. 


lift. 


12 ft. 


13 ft. 


14 ft. 


15 ft. 16 ft. 


17 ft. 


18 ft. 




inch. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 




4 


2-1 


2-3 


2-5 


2-7 


3-0 


3-2 


3-4 


3-6 


3-8 




§ 


4-8 


5-2 


5-7 


6-2 


6-7 


7-1 


7-6 


8-1 


8-6] 




h 


8-5 


9-3 


10-1 


11-0 


11-8 


12-0 


13-5 


14-4 


15-2] 




1 


13-2 


14-5 


15-8 


17-2 


18-5 


19-8 


211 


22-4 


23-8 




1 


19-0 


20-9 


22-8 


24-7 


26-6 


28-5 


30-4 


32-3 


34-2; 




i 


25-9 


28-5 


31-1 


33-6 


36-2 


W-8 


414 


44-0 


46-6 






l 


33-8 


37-2 


40-6 


43-9 


47-3 


50-7 


541 


57-5 


60-8 






u 


42-8 


471 


51-3 


55-6 


59-9 


64-2 


68-4 


72-7 


77-0 






n 


52-8 


58-1 


63-4 


68-6 


73-9 


79-2 


84-5 


89-8 


95-0 






h 


63-9 


70-3 


76-7 


83-1 


89-5 


95-9 


102-2 


108-6 


115-0 






14 


76-0 


83-6 


91-2 


98-9 


106-5 


114-1 


121-7 


129-3 


136-9 






1 8 S 


89-3 


98-2 


107-1 


1160 


125-0 


133-9 


142-8 


151-7 


160-7 






11 


103-5 


133-9 


124-2 


134-6 


144-9 


155-3 


165-6 


176-0 


186-3 






H 


118-8 


130-7 


142-6 


154-5 


166-4 


178-2 


190-1 


202-0 


213-9 






2 


135-2 


148-7 


162-2 


175-8 


183 3 


202-8 


216-3 


229-8 


243-4 






2£ 


152-G 


167-9 


183-2 


198-4 


213 7 


228 9 


244-2 


259-5 274 1 






2i 


171-1 


188-2 


205-3 


222-5 


239 6 


2567 


273-8 


290-9 


30v«-«i 




21 


190-7 


209-7 


228-8 


247-9 


266-9 


286-0 


3051 


324-1 


343-2 






24 


211-2 


232-3 


253-4 


274-6 


295-7 


316-8 


337-9 


359-0 


380-2 






2| 


232-9 


256-2 


279-5 


302-8 


326-1 


349-4 


372-7 


396-0 


419-3 






2| 


255-6 


281-2 


306-7 


332-3 


357-8 


383-4 


409-0 


434-5 


460-1 






2& 


279-4 


307-3 


335 3 


363-2 


391-1 


419-1 


447-0 


475-0 


502 9 






3 


304-2 


334-6 


365-0 


395 4 


425-8 


456-2 


486-7 


517-1 


547 5 






3J 


330-1 


363-1 


396-1 


429-1 


462-1 


495-2 


528-2 


561-2 


594-2 




3i 


357-0 


392-7 


428-4 


464-2 


499-9 


535-6 


571-3 


607-0 


642-7 




31 


385-0 


423-5 


462-0 


500-5 


539-0 


577-5 


616-0 


654-6 


693-1 1 




34 


414-1 


455-5 


496-9 


538-3 


579-7 


621-1 


662-5 


703-9 


745-3 1 




3| 


444-2 


488-6 


533-0 


577-4 


621-9 


666-3 


710-7 


755-1 


799-5 1 




32 


475-3 


522-9 


570-4 


617-9 


665-5 


713-0 


760-5 


808-1 


855-6| 




35 


507-6 


558-3 


609-1 


659-8 


710-6 


761-3 


812-1 


862-9 


913-61 


1 






10* 


I 

1 i 



12 PRACTICAL TABLES. 

TABLE I. — SQUARE IRON. 



size. 


1ft. 


2 ft. 


3 ft. 


4ft. 


5ft. 


6 ft. 


7ft 


8 ft. 


! 

9ft. 


inch 


lbs. 


lbs. 


lbs. 


Ibs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


4 


54-1 


108-2 


162-3 


216-3 


270-4 


324-5 


378-6 


432-7 


486-8 


u 


57-5 


115-0 


172-6 


230-1 


287-6 


345-1 


402-6 


460-1 


517-7 


4* 


61-1 


122-1 


183-2 


244-2 


305-3 


366-3 


427-4 


488-4 


549-5 


4| 


64-7 


129-4 


194-1 


258-8 


323-5 


388-2 


452-9 


517-6 


5823 


u 


68-4 


136-9 


205-3 


273-8 


342-2 


410-7 


479-1 


547-6 


616-0 


4| 


72-3 


144-6 


216-9 


289-2 


361-5 


433-8 


506-1 


578-4 


650-7 


4| 


76-3 


152-5 


228-8 


305-1 


381-3 


457-6 


533-8 


610-1 


686-4 


41 


80-3 


160-7 


241-0 


321-3 


401-7 


482-0 


562-3 


642-7 


723-0 


5 


84-5 


169-0 


253-4 


337-9 


422-4 


506-9 


591-4 


675-8 


760-3 


54 


88-8 


177-G 


266-4 


355-1 


443-9 


532-7 


621-5 


710-3 


799-1 


54 


93-2 


186-3 


279-5 


372-7 


465-8 


559-0 


652-2 


745-3 


838-5 


51 


97-7 


195-3 


293-0 


390-6 


488-3 


585-9 


683-6 


781-3 


878-9 


5i 


102-2 


204-5 


306-7 


409-0 


511-2 


613-4 


715-7 


817-9 


920-2 


5| 


107-0 


213-5 


320-9 


427-8 


534-8 


641-7 


748-7 


855-6 


962-6| 


5| 

5* 


111-8 


223-5 


335-3 


447-0 


558-8 


670-5 


782-3 


894-0 


1005-8 


116-7 


233-3 


350-0 


466-7 


583-4 


700-0 


816-7 


933-4 


1050-0 ! 


6 


121-7 


243-3 


365-0 


486-7 


608-3 


730-0 


841-6 


973-3 


1095-0 


6£ 


132-0 


264-1 


396-1 


528-2 


660-2 


792-2 


924-3 


1056-3 


1 188-4 ; 


6d 


142-8 


285-6 


428-4 


571-3 


714-1 


856-9 


999-7 


1142-5 


1285-3 


G| 


151-0 


308-0 


462-0 


616-0 


770-1 


9241 


1078-1 


1232-1 


1386-1 i 


7 


165-6 


331-2 


496-9 


662-5 


828-2 


993-8 


1159-4 


1325-1 


1 490-7 \ 


71 


177-7 


355-3 


533-0 


710-7 


888-4 


1066-0 


1243-7 


1421-4 


1599-0 


7h 


190-1 


380-3 


570-4 


760-5 


950-7 


1140-8 


1331-0 


1521 1 


1711-2 


71 


203-0 


406-0 


609-1 


812-1 


1015-1 


1218-1 


1421-2 


1624-2 


1827-2 


8 


216-3 


432-7 


649-0 


865-3 


1081-7 


1298-0 


1514-4 


1730-7 


1947-0 


84 


23)-l 


460-1 


690-2 


920-3 


1150-3 


1380-4 


1610-5 


1840-5 


2070-6 


8i 


244-2 


488-4 


732-7 


976-9 


1221-1 


1465-3 


17095 


1953-8 


2198-0 


8| 


25S-8 


517-6 


776-4 


1035-2 


1294-0 


1552-8 


1811-6 


2070-4 


2329-2 


9 


273 8 


547-6 


f21-4 


1095-2 


1369-0 


1642-8 


1916-5 


2190-3 


2464-1 












- ' ' J 



PRACTICAL TABLES. 



113 



TAI1LE I.-SQUARE IRON. 



1 

size. 


10 ft. 


lift. 12 ft 


13 ft 


14ft.l5ft. 


16 ft 


17 ft. 


18 ft. 


inch 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. lbs. 


lbs. 


lbs. 


lbs. 


4 


540-8 


594-9 


649-0 


703-1 


757-2 811-3 


865-C 


919-4 


973-5 


4* 


575-2 


632-7 


690-2 


747-7 


805-2 1 862-8 


920-L 


977-8 


1035-3 


4* 


610-6 


671-6 


732-7 


793-7 


854-8 915-8 


976-9 


1037-9 


1099-0 


48 


646-0 


711-7 


776-4 


841-1 


905-8 970-5 


1035-2 


1099-9 


1164-6 


Ah 


684-5 


752-9 


821-4 


889-8 


958-3 '1026-7 


1095-2 


1 J 63-6 


1232-1 


4§ 


723-1 


795-4 


867-7 


940-0 


1012-3 1084-6 


1156-9 


1229-2 


1301-5 


41 


762-6 


838-9 


915-2 


991-4 


1067-7 1144-0 


1220-2 


1296-5 


1372-8 


44 


803-3 


883-7 


964-0 


1044-3 


1124-7 


1205-0 


1285-3 


1365-7 


1446-0 


5 


844-8 


929-3 


1013-8 


1098-2 


1182-7 


1267-2 


1351-7 


1436-2 


1520-6 


5k 


887-8 


976-6 i 1065-4 


1154-2 


1243-0 1331-8 


1420-5 


1509-3 


1598-1 


H 


931-7 


1024-8 1118-0 


1211-2 


1304-4 j 1397-5 


1490-7 


1583-9 


1677-0 


1 5» 


976-6 


1074-2 


1171-9 


1269-5 


1367-2 1464-9 


1562-5 


1660-2 


1757-8 


i>4 


1022-4 


1124-6 


1226-9 


1329-1 


1431-4 1533-6 


1635-8 


1738-1 


1840-3 


H 


1069-5 


1176-5 


1283-4 


1390-4 


1497-3 1604-3 


1711-2 


1818-2 


1925-2 


5i 
51 


1117-6 


1229-3 


1341-1 


1452-8 


1564-6 


1676-3 


1788-1 


1899-9 


2011-6 


1160-0 


1283-4 


1400-1 


1516-7 


1633-4 


1750-1 


1866-7 


1983-4 


2100-1 


6 


1229 6 


1338-3 


1460-0 


1581-6 


1703-3 


1825-0 


1946-6 


2068-3 


2190-0 


(4 


1320-4 


1452-4 


1584-4 


1716-5 


1848-6 1980-6 


2112-6 


2244-7 


2376-7 


b£ 


1428-2 


1571-0 


1713-8 


1856-6 


1999-4 2142-2 


2285-1 


2427-9 2870-7 


6* 


1540-1 


1694-1 


1848-1 


2002-2 


2056-2 2310-2 


2464-2 


2618-2 j 2772-2 


7 


1656-3 


1822-0 


1987-6 


2153-2 


2318-8 2184-5 


2650-1 


2815-7 2981-4 


7i 


1776-7 


1954-4 


21321 


2309-7 


2487-4 2665-1 


2842-8 


3020-4 3198-1 


7i 


1901-4 


2091-5 


2281-6 


2471-8 


2661-9 2852-0 


3042-2 


3232-3 1 34-22-4 


yi 


2030-2 


2233-3 


2436-3 


2639-3 


2842-3 j 3045-4 


3248-4 


3451-4 


3654-4 


8 


2163-4 


2379-7 


2596-0 , 


2812-4 3028-7 .3245-0 


34CI-4 


3677-7 


3894-0 


84 


2300-7 


2530-7 


2760-8, 


2990-9,3220-9 3451-0 


3681-1 


3911-1 


1141-2 


fctf 


2442-2 


2686-4 


2930-6 


31 74-9 1 341 9- 1| 3663-3 


3907-5 


4151-7 


1396-0 


H4 


2588-0 


2846-8 


3105-6 


H64-4 3623-2 3882-0 


4140-8 


4399-6 4658-4 


(9 


2737-9 


3011-7 


3285-5 


3559-3^33-1 14106-9 


13807 


4654-5 [4928-3 



Ml PRACTICAL TABLES 

TABLE I. — SQUARE IRON 



size. 


in. 


2ft. j 3ft. 


4ft. 


5ft. 


6 ft. 


7ft 


8 ft. 


lbs. 


inch. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 




289-2 


578-4 


867-7,1156-9 1446-1 


1735-3 


2024-5 


2313-8 


2003-0 


305-1 


610-1 915-2 


1220-2 1525-3 


1830-3 


2135-4 


2440-4 


2745-5 


91 


321-3 


642-7 


964-0 


1285-3 


1606-7 


1928-0 


2249-3 


2570-7 


2892-3 


10 


337-9 


675-8 


1013-8 


1351-7 


1689-6 


2027-5 


2365-4 


2703-4 


3041-0 


104 


355-1 


710-3 


1065-4 


1420-5 


1775-7 


2130-8 


2486-0 


2841-1 


3190-2 


104 


372-7 


745-3 


1118-0 


1490-7 1863-4 


2236-0 


2008-7 


2981-4 


3354-0 


101 


390-6 


781-3 


1171-9 


1562-5 


1953-1 


2343-8 


2734-4 


3125-0 


3515-7 


11 


409-0 


817-9 


1226-9 


1635-8 


2044-8 


2453-8 


2862-7 


3271-7 


3680-6 


114 


427-8 


855-6 


1283-4 


1711-2 2139-1 


2566-9 


2994-7 


3422-5 


3850-3 


Hi 


447-0 


894-0 


1341-1 


1788-1 2235-1 


2682-1 


3129-2 


3576-2 


4023-2 


114 


466*7 


933-4 


1400-1 


1866-7 2333-4 


2800-1 


3266-8 


3733-5 


4200-2 


* 


486-7 


973-3 


1460-0 


1946-6 2433-3 


2919-9 


3406-6 


3893-2 


4379* 



PRACTICAL TABLES. 115 

TABLE 1 — SaUARE IRON. 



size. 


10 ft 


lift. 


12 ft. 


13 ft 


14 ft 


15 ft 


lGft 


17 ft 


18 ft 


inch. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


<n 


2892-2 


3181-4 


3470-6 


3759-9 


4049-1 


4338-3 


4627-5 


4916-7 5206-0 


<u 


3050-6 


3355-6 


3660-7 


3965-7 


4270-8 


4575-8 


4880-9 


5186-0 15491-0 


91 


3213-3 


3534-7 


3856-4 


4177-3 


4498-6 


4820-0 


5141-3 


5462-6 


57810 


10 


3379-2 


3717-1 4055-0 


4393-0 


4730-9 


5068-8 


5406-7 


5744-6 


6082-G 


10* 


3551-4 


3906-5 4261-6 


4616-8 


4971-9 


5327-0 


5682-2 


6037-3 


6392-4 


10i 


372G-7 


4099-4 4472-1 


4844-7 


5217-4 


5590-1 


5962-8 


6335-4 


6708-1 


10| 


3906-3 


4297-0 4687-5 


5078*2 


5468-8 


5859-4 


6250-0 


6644-7 


7031-3 


11 


4089-G 


4498-6 4907-5 


5316-5 


5725-4 


6134-4 


6543-4 


6952-3 


7361-3 


111 


4278-1 


4705-9 5133-7 


5561-6 


5989-4 


6417-2 


6845-0 


7272-8 


7700-6 


Hi 


4470-2 4917-3 1 5364-3 


5811-3 
606<r9 


6958-3 


6705-4 


7152-4 


7599-4 


8046-4 


111 


4666-8 


5133-5 5600-2 


6533-6 


7000-3 


7466-9 


7933-6 


8400-3 


12 


4866-6 


5353-2 5839-9 


6326-5 


6813-2 


7299-8 


7786-5 


8273-2 


8759-8 





116 






PRACTICAL TABLES. 
















TABLE I 


I.— ROUND HON. 






! 


size. 


1ft. 


2ft. 


3ft. 


4ft. 


5 ft. 


6ft. 


7ft. 


8ft.. 


9ft. 


inch. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs 


lbs. 




| 


0-2 


0-3 


0-5 


0-7 


0-8 


1-0 


1-2 


1-3 


1.5 






i 


0-4 


0-7 


1-1 


1-5 


1-9 


2-2 


2-6 


30 


3-4 






i 


0-7 


1-3 


2-0 


2-7 


3-3 


4-0 


4-6 


5-3 


60 






i 


1-0 


21 


31 


4-2 


5-2 


6-3 


7-3 


8-3 


3 4 






I 


1-5 


3-0 


4-5 


6-0 


7-5 


9-0 


10-5 


11-9 


13-4 






i 


2-0 


4-1 


6-1 


8-1 


10-2 


12-2 


14-2 


16-3 


18-3 








2-7 


5-3 


8-0 


10-6 


13-3 


15-9 


18-6 


21-2 


23-9 






l* 


3-4 


6-7 


10-1 


13-4 


16-8 


20-2 


23-5 


26-9 


30-2 






H 


4-2 


8-3 


12-5 


16-7 


20-9 


25-0 


29-2 


33-4 


37-5 






H 


5-0 


10-0 


15-1 


20-1 


25-1 


>0-l 


35-1 


40-2 


45-2 






II 


6-0 


11-9 


17-9 


23-9 


29-9 


35-8 


41-8 


47-8 


53-7 






l| 


7-0 


14-0 


21-0 


28-0 


35-1 


42-1 


49-1 


56-1 


63-1 






U 


8-1 


16-3 


24-4 


32-5 


40-6 


48-8 


56-9 


65-0 


73 2 






H 


9-3 


18-7 


28-0 


37-3 


46-7 


56-0 


65-3 


74-7 


84-0 






2 


10-6 


21-2 


31-8 


42-5 


53-1 


63-7 


74-3 


84-9 


95-5 






2& 


12-0 


240 


36-0 


480 


59-9 


71-9 


83-9 


95-9 


107-9 






21 


13-5 


26-9 


40-3 


53-8 


67-2 


80-6 


941 


107-5 


121-0 






21 


15-0 


30-0 


44-9 


60-0 


74-9 


89-9 


104-8 


119-8 


134-8 






24 


16-7 


33-4 


501 


66-8 


83-4 


100-1 


116-8 


133-5 


150-2 






21 


18-8 


36-6 


54-9 


73-2 


91-5 


109-8 


128-1 


146-3 


164 6 






21 


20-1 


40-2 


60-2 


80-3 


100-4 


120-5 


140-5 


160-6 


180-7 






2i 


21-9 


43-9 


65-8 


87-8 


109-7 


131-7 


153-6 


175-6 


197-5 






3 


23-9 


47-8 


71-7 


95-6 


119-4 


143-3 


167-2 


191 1 


215 






3J 


25-9 


51-9 


77*8 


103-7 


129-6 


155-6 


181-5 


207-4 


233-3 






34 


28-0 


56-1 


84-1 


112-2 


140-2 


168-2 


196-3 


224-3 


253-4 






31 


30-2 


60-5 


90-7 


121-0 


151-2 


181-4 


211-7 


24H 


272-2 






3i 


32-5 


65-0 


97«5 


10-0 


162-6 


195-1 


227-6 


260-1 


293-6 






31 


34-9 


69-8 


104-7 


139-5 


174-4 


209-3 


244-9 


279-1 


314-0 






31 


37-3 


74-7 


I'M 


149-3 


186-7 


224-0 


261-3 


298-7 


336-0 






Si 


39-9 


79-7 


» 


159-5 


199-3 


239-2 


279-0 


318-9 


358-8 

j 





PRACTICAL TABLES. 
T^BLE II.-RO"ND IRON. 



11/ 



1 

1 size. 


10 ft. 


lift. 


12 ft. 


13 ft. 


14 ft, 


15 ft. 1 16 ft. 


17 ft. 


18ft. 


/inch. 


lbs. 


lbs. 


lbs. 


lba. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


4 


1-7 


1-8 


2-0 


2-1 


2-3 


2-5 


2-6 


2-8 


30 


1 


3-7 


4-1 


4-5 


4-8 


5-2 


5-6 


6-0 


6-3 


6-7 


h 


6-6 


7-3 


8-0 


8-6 


9-3 


9-1 1 


10-6 


11-3 


11-9 


I 


10-4 


11-5 


12-5 


13-6 


14-6 


15-6 


16-7 


i7-3 


18-8 


1 


14-9 


16-4 


17-9 


19-4 


20-9 


22--? 


23-9 


25-4 


26-9 


i 


20-3 


22-4 


24-4 


26-4 


28-4 


30-5 


32-5 


34-5 


366 


1 


26-5 


29-2 


31-8 


34-5 


37-2 


39-e 


42-5 


45-1 


47 8 


n 


33-6 


37-0 


40-3 


43-7 


47-0 


50-4 


53-8 


57-1 


60 5 


14 


41-7 


45-9 


50-1 


54-2 


58-4 


62-6 


66-8 


70-9 


75 1 


If 


50-2 


55-2 


60-2 


65-2 


70-3 


75? 


80-3 


85-3 


90-3 


H 


59-7 


65-7 


71-7 


77-6 


83-6 


89-6 


95-6 


101-5 


107 5 


H 


70-1 


77-1 


84-1 


91-1 


98- 1 


105-2 


1 12-2 


.19-2 


J26 2 


11 


81-3 


89-4 


97-5 


105-7 


113-8 


121-9 


130-0 


138-2 


146-3 


H 


93-3 


102-7 


112-0 


121-3 


130-7 


140-0 


119-3 


J 58-7 


168 


2 


106-2 


116-8 


127-4 


138-0 


148-6 


159-2 


169-9 


180-5 


! 
192 1 


2* 


119-9 


131-9 


143-9 


155-8 


167-8 


179-8 


181-8 


193-8 


205-8| 


24 


134-4 


147-8 


161-3 


174-7 


188-2 


201-6 


215-0 


228-5 


241-9 


21 


149-8 


164-7 


179-7 


194-7 


209-7 


224-6 


239-6 


254-6 


269-6 


24 


166-9 


183-6 


200-3 


216-9 


233-6 


250-3 


267-0 


283-7 


300-4 


21 


i82-9 


201-2 


219-5 


237-8 


256-1 


274-4 


292-7 


311-0 


329-3 


24 


JOO-8 


220-8 


240-9 


261-2 


281-1 


301-1 


321-2 


341-3 


361-4 


2i 


219-4 


241-4 


263-4 


285-3 


307-2 


329-2 


351-1 


373-0 


395-0 


J 


^38-9 


262-8 


286-7 


310-5 


334-4 


358-3 


382-2 


406-1 


430-0 


OJ 


259-3 


285-2 


311-1 


337-0 


363-0 


388-9 414-8 


440-7 


466-7 


34 


280-4 


308-4 


336-5 


364-5 


392-6 


420-6 448-6 


476-7 


504-7 


3| 


302-4 


332-6 


362-9 


393-1 


423-4 


453-6 


483-8 


514-1 


544-3 


% 


325-1 


357-6 


390-1 


422-7 


455-2 


487-7 


520-2 


552-7 


585-2 


38 


348 9 


383-7 


418-6 


453-5 


488-4 


523-3 


558-2 


593-1 


627-9 


M 


3733 


410-7 


448-0 


485-3 j 


522-6 


560-0 


597-31 


634-6 


672-0 


^k 


398 6 
1 


438-5 


478-4 
1 


518-2 
1 


558-1 


598-0, 637-8, 677-7 

I 1 


717-6 



fr~ — 

118 




PRACTICAL TABLES. 






TABLE 11. — ROUND IRON 






size. 


1ft. 


2ft. 


3ft. 


4ft. 


5 ft. 


6 ft. 


7ft. 


8ft. 


9ft. 




inch. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 




4 


42-5 


84-9 


127-4 


169-9 


212-3 


254-8 


297-2 


339-7 


382-2 






4* 


45-2 


90-3 


135-5 


180-7 


225-9 


271-0 


316-2 


361-4 


406-6 






4* 


48-0 


95-9 


143-9 


191-8 


239-8 


287-7 


335-7 


383-6 


431-6 






4| 


50-8 


101-6 


152-4 


203-3 


254-1 


304-9 


355-7 


406-5 


457-3 






44 


53-8 


107-5 


161-3 


215-0 


268-8 


322-6 


376-3 


430-1 


483-8 






41 


56-8 


113-6 


170-4 


227-2 


283-9 


340-7 


397-5 


454-3 


511-1 






41 


60-0 


119-8 


179-7 


239-6 


299-5 


359-4 


419-3 


479-2 


539-1 






4§ 


63-1 


126-2 


189-3 


252-4 


315-5 


378-6 


411-7 


504-8 


567-8 






5 


66-8 


133-5 


200-3 


267-0 


333-8 


400-5 


467-3 


534-0 


600-8 






51 


69-7 


139-5 


209-2 


278-9 


348-7 


418-4 


488-1 


557-8 


627-6 






5* 


73-2 


146-3 


219-5 


292-7 


365-9 


439-0 


512-2 


585-4 


658-5 






5i 


76-7 


153-4 


230-1 


306-8 


383-5 


460-2 


536-9 


613-6 


690 3 






5£ 


80-3 


160-6 


240-9 


321-2 


401-5 


481-8 


562-1 


642-4 


722-7 






5£ 


84-0 


168-0 


252-0 


336-0 


42O-0 


504-0 


588-0 


672-0 


756-0 






5| 


87-8 


175-6 


263-3 


351-1 


438-9 


526-7 


614-4 


702-2 


790-0 






5J 


91-6 


183-3 


274-9 


366-5 


458-2 


549-8 


641-4 


733-1 


824-7 






6 


95-6 


191-1 


286-7 


382-2 


477-8 


573-3 


668-9 


764-4 


860-0 






61 


103-7 


207-4 


311-1 


414-8 


518-5 


622-2 


725-9 


829-6 


933-3 






6i 


112-2 


224-3 


336-5 


448-6 


560-8 


673-0 


785-1 


897-3 


1009-4 






61 


121-0 


241-9 


362-9 


483-8 


604-8 


725-8 


846-7 


967-6 


1088-6 






7 


130-0 


260-1 


390-1 


520-2 


650-2 


780-3 


910-3 


1040-4 


1170-4 






7i 


139-5 


279-1 


418-6 


558-2 


697-7 


837-3 


976-8 


1116-4 


1255-9 






7| 


149-3 


298-7 


448-0 


597-3 


741-6 


896-0 


1045-3 


1194-6 


1344-0 






7| 


159-5 


318-9 


478-4 


637-8 


797-3 


956-7 


1116-2 


1275-6 


1435-1 






8 


169-9 


339-7 


509-6 


679-4 


849-3 


1019-1 


U89-0 


1358-8 


1528-7 






8* 


180-7 


361-4 


542-1 


722-8 


003-5 


1084-2 


1264-9 


1445-6 


1626-3 






r s 


191-8 


383-6 


595-4 


767-2 


959-0 


1150-8 


1342-6 


1534-5 


1726-3 






8| 


203-3 


406-5 


609-8 


813-0 


1016-3 


1219-6 


1422-8 


]£26-l 


1829-3 




i 


9 


2150 


430-1 

> 


645-1 


860-2 


1075-2 


1290-2 


1505-3 


1720-3 


1935-4 





TRACTICAl Af>,.^S. I ID 

TABLE II. — ROUND IRON. 



T- 

| size. 


10 ft. 


lift. 


12 ft. 


13 ft. 


14 ft 


15 ft.' 16 ft 


17 ft. 


is a 


inch. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. lbs. 


lbs. 


lbs. 


4 


424-6 


467-1 


509-6 


552-0 


594-5 


637-0' 676-4 


721-9 


764-4 


4$ 


451-7 


496-9 


542-1 


587-3 


632-4 


677-6 J 722-8 


7619 


813-1 


44 


479-5 


527-5 


575-4 623-4 


671-3 


719-3 767-2 j 815 2 


863-1 


41 


508-2 


559-0 J 609-8 


660-6 


711-4 


762-2 813-0 863-9 


914-7 


U 


537-6 


591 -4 J 645-1 


698-9 


752-!) 


806-4 860-21 913-9 


967-7 


4f 


567-9 


624-7 1 681-5 


738-2 


795-0 851-8 908-6 1 965-4 


1022-2 


41 


599-0 


658-9 


718-8 


778-7 


838-b 


898-5, 958-4| 1018-3 


1078-2 


4& 


630-9 


694-0 


757-1 


820-2 


883-3 


946-4 1009-5 


1072-6 


1135-7 


5 


667-5 


734-3 


801-0 


867-8 


934-5 


1001-3 1068-0 


11134-8 


1201-5 


5| 


697-3 


767-0 


836-8 


906-5 


976-2 


J 046-0 1115-7 


1 185-4 


1255-2 


5* 


731-7 


804-9 


878-1 


951-2 


1024-4 


1097-6 1170-8 


1243-9 


1317-1 


51 


767-0 


813-7 


920-4 


997-1 


1073-8 


1150-5 1227-2 


1303-9 


1380-6 


oh 


803-0 


883-3 


963-6 


1044-0 


1124-3 


1204-6 1284-9 


1365-2 


1445-5 


H 


840 


924-0 


1008-0 


1092-0 


1176-0 


1260-0 1344-0 


1428-0 


R12-0 


53 


877-8 


965-5 


1053-3 


1141-1 


1228-9 


1316-6 1404-4 


1492-2 


1580-0 


916-3 


1008-0 


1099-6 


1191-2 


1282-9 


1374-5 1466-1 


1557-8 


1649-4 


6 


955-5 


1051-1 


1146-6 


1242-2 


1337-7 


i 

1433-3 1528-8 


1624-4 


1719-9 


64 


1037-0 


1140-7 


1244-4 


1348-2 


1451-9 


1555-6 1659-3 


1763-0 


1866-7 


G£ 


1121-6 


1233-8 


1345-9 


1458-1 


1570-2 


1682-4 1794-6 


1906-7 


2018-0 


63 


1209-6 


1330-6 


1451-5 


1572-5 


1693-4 


1814-4 1935-4 

1 


2056-3 


2177-3 


7 


1300-5 


1430-5 


1560-6 


1690-6 


1820-7 


1 
1950-7 2088-8 


2210-8 2340-9 


74 


1395-4 


1535-0 


1674-5 


1814-1 


1953-6 


2093-2 2232-7 


2372-212511-8 


74 


1493-3 


1642-6 


1791-9 


1941-3 


2090-6 


2239-9 2389-2 


2538-6 2687-9 


73 


159-.6 


1754-0 


1913-5 


2072-9 


2232-4 


2391-8 2551-3 

1 


2710-8 2870-2 


8 


1698-6 


1868-4 


2038-3 


2208-1 


2378-0 


1547-8 2717-7 


2887-6 13057-4 


84 


1809-0 


1987-7 


2168-4 


2349-0 


2529-7 


2740-4 2891-1 


3071-8 3252-5 


Sh 


1918-1 


2109-9 


2301-7 


2493-5 


2685-3 


2879-1 3068-9 


3260-7 


3452-5 


83 


2032-6 


2235-9 


2439-1 


2642-4 


2845-6 


3048-9 3252-2 


3455-4 


3653-7 


9 


2150-4 


2365-4 


2580-5 


2795-5 


3010 6 


1 
3225-6 3440-6 


3655-7 


3870-7 



11 



20 PRACTICAL TABLES. 

TABLE II. — HOUND IKON. 



size. 


1ft. 


2 ft. 


3 ft. 


4 ft 


5 ft. 


6 ft. 


7ft 


8ft 


9ft. 


inch. 


lbs. 


lbs. 


Ib3. lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs 


9* 


227-2 454-3 


681-5 ' 908-6 


1135-8 


1362-9 


15901 


1817-2 


2044 4 


239-6 


479-2 718-8: 958-4 


1198-0 1437-6 


1677-2 


1916-8 


2156-4 


9| 


252-4 


505-8 


757-1 i 1009-5 


1261-91 1514-3 


1766-6 


2019-0 


2291-4 


10 


26G-3 


532-6 


798-9: 10C5-2 


1331-4 1597-7! 1864-0 


2130-3 


2396-6 


104 


278-9 


557-8 


836-8 11 U.-7 


1394-6 


1673-5| 1952-5 


2231-4 


2510-3 


10* 


292-7 


585-4 


878-1 1 1170-8 


1463-4 


1756-1 2048-8 


2341-5 


2634-2 


10| 


306-8 


603-6 


920-4 1 1227-2 


1534-0 


1840-8 2147-6 


2454-4 


2761-2 


11 


321-2 


642-4 


963-6 1284-9 


1606-1 


1927-3 2248-5 


2569-7 


2890-9 


Hi 


336-0 


672-0 


1008-0 1344-0 


1680-0 


2016-0 


2352*0 


2688-0 


3024-0 


Hi 


3511 


702-2 


1053-3 


1404-4 


1755-5 


2106-6 


2457-7 


2808-8 


3159-9 


m 


366-5 


733-1 


1099-6 


14-56-1 


1832-7 


2199-2 


2565-8 


2932-3 


3298-8 


12 


382-2 


764-4 


1146-6 


1528-8 


1911-0 


2293-2 


2675-5 


3057-7 


3439-9J 



PRACTICAL TABLES. 121 

TABLE II. — ROUND IRON. 



size. 


10 «. 


lift. 


12 ft. 


13 ft. 


14 ft. 


15 ft. 


16 ft. 


17 ft. 


18 ft. 


inch. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. lbs. 


lbs. 


lbs. 


94 


2271-5 2498-7 


2725-8 


2953-0 


3180-1 


3407-3 1 3634-4 


3861-6 


4088-7 


94 


2396-0 2635-6 


2875-2 


3114-8 


3354-4 


3594-0 


3833-6 


4073-2 


4312-8 


m 


2523-8 1 2776-1 


3028-5 


3280-9 


3533-3 


3785-6 


4038-0 


4290-4 


4512-8 


10 


2662-9 2929-2 


3195-5 


3461-7 


3728-0 


3994-3 


4260-6 


4526-9 


4793-2 


10* 


2789-2 


3068-2 


3347-1 


3626-0 


3904-9 


4183-9 


4462-8 


4741-7 


5020-6 


10i 


2926-9 


3219-6 


3512-3 


3804-9 


4097-6 


4390-3 


4683-0 


4975-7 


5268-4 


101 


3068-0 


3374-8 


3681-6 


3988-4 


4295-2 


4602-0 


4908-8 


5215-6 


5522-4 


11 


3212-2 


3533-4 


3854-6 


4175-8 


4497-0 


4818-2 


5139-5 


5460-7 


5781-9 


iii 


3360-0 


3696-0 


4032-0 


4368-1 


4704-1 


5040-1 


53761 


5712-1 


6048-1 


1U 


3511-0 


3862-1 


4213-2 


4564-4 


4915-5 


5266-6 


5619-7 


5968-8 


6319-9! 


m 


3665-4 


4031-9 


4398-4 


4765-0 


5131-5 


5498-0 


5864-6 


62311 


6597-6 


12 


3822-1 


4204-3 


4586-5 


4968-7 


5350-915733-1 


6115-3 


6497-5 


6879-7J 



22 






PRACTICAL TABLES. 






TABLE III FLAT IRON. 






Th'k. 


Wid. 


1ft 


2ft 


3ft 


4ft 


5ft 


6ft 


7ft 


8ft 


9ft 




inch. 


inch. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 




4 


1 


0-8 


1-7 


2-5 


3-4 


4-2 


5-1 


5-9 


6-8 


76 






k 


u 


1-1 


O. | 


3-2 


4-2 


5-3 


6-3 


7-4 


8-4 


9-5 






i 


u 


14 


2-5 


3-8 


5-1 


6-3 


7-6 


8-9 


10-1 


114 






I 


u 


1-5 


3-0 


4-1 


5-9 


7-4 


8-9 


10-4 


11-8 


13-3 






i 


2 


1-7 


3-4 


5-1 


6-8 


8-5 


10-1 


11-8 


13-5 


15-2 






4 


24 


1-9 


3-* 


5-7 


7-6 


9-5 


11-4 


13-3 


15-2 


17-1 






I 


24 


2-1 


4-2 


6-3 


8-4 1 10-6 


12-7 


14-8 


16-9 


19 






k 


21 


2-3 


4-6 


7-o 


9-:? 11-G 


13-9 


16-3 


18-6 


20 9 






I 


3 


2-5 


5-1 


7-6 


10-1 12-7 


15-2 


17-7 


20-3 


228 






4 


34 


2-7 


5-5 


8-2 


11-0 


13-7 


16-5 


19-2 


22-0 


24-7 






k 


34 


3-0 


5-9 


8-9 


11-8 


14-8 


17-7 


20-7 


23-7 


26-6 






4 


31 


3-2 


6-3 


9-5 


12-7 


15-8 


19-0 


22-2 


25-4 


28-5 






k 


4 


3-4 


6-8 


10-1 


13-5 


16-9 


20-3 


23-7 


27-0 


30-4 






k 


44 


3-6 


7-2 


10-8 


14-4 


18-0 


21-5 


25-1 


28-7 


32-3 






k 


4i 


3-8 


7-6 


11-4 


15-2 


19-0 


22-8 


26-6 


30-4 


34-2 






k 


41 


4-0 


8-0 


120 


16-1 


20-1 


24-1 


28-1 


32-1 


36-1 






k 


5 


4-2 


8-4 


12-7 


16-9 


211 


25-3 


29-6 


33-8 


38-0 






k 


54 


4-4 


8-9 


13-3 


17-7 


22-2 


26-6 


31-1 


av5 


39-9 






k 


54 


4-6 


9-3 


13-9 


18-6 


23-2 


27-9 


32-5 


37-2 


41-8 






k 


51 


4-9 


9-7 


14 6 


19-4 


24-3 


29-2 


34-0 


38-9 


43-7 






k 


6 


5-1 


10-1 


15-2 


20-3 


25-3 


30-4 


35-5 


40-6 


45-6 






I 
1 
1 

§ 


1 


1-3 


2-5 


3-8 


5-1 


6-3 


7-6 


8-9 


10*1 


11-4 






14 
U 


1-6 


3-2 


4-8 


6-3 


7-9 


9-5 


11-1 


12-7 


14-3 






1-9 


3-8 


5-7 


7-6 


9-5 


11-4 


13-3 


15-2 


171 






u 


2-2 


4-4 


6-7 


8-9 


111 


'«3-3 


15-5 


17 7 


20-0 






1 
1 


2 


2-5 


51 


7-6 


10-1 


12-7 


15*2 


17-7 


20-3 


22-8 






24 


2-9 


5-7 


8-3 


11-4 


14-3 


1M 


20-0 


22-8 


25-7 






§ 


24 


3-2 


6-3 


9-5 


12-7 


15-8 


19-0 


22-2 25-4 


28-5 

















, 



PRACTICAL TABLES. 123 

TABLE III —FLAT IRON. 



Th'k. 


Wid. 


jlOft lift 

1 


12ft 13ft 14ft 


15ft 


16'ft 


17ft 


18ft 


Inch. 


inch. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 




1 


8-5 


9-3 


10-i 


110 


11-8 


12-7 


13-5 


14-4 


15-2 




n 


10-6 


11*6 


12-7 


13-7 


14-8 


15-8 


16-9 


17-9 


19-0 




n 


12-7 


13-9 


15-2 


16-5 


17-7 


19-0 


20-3 


21-5 


22-8 




if 


14-8 


16-3 


17-7 


19-2 


20-7 


22-2 


23-7 


25-1 


26-6 




2 


16-9 


18-6 


20-3 


22-0 


23-7 


25-4 


27-0 


28-7 


30-4 




24 


19-0 


20-9 


22-8 


24-7 


2(5-6 


28-5 


30-4 


32-3 


34-2 




n 


21-1 


23-2 


25-3 


27-5 


29-6 


31-7 


33-8 


35-9 


38-0 




2| 


23-2 


25-6 


27-9 


30-2 


32-5 


34-9 


37-2 


39-5 


41-8 




3 


2S*3 


27-9 


30-4 


33-0 


35-5 


38-0 


40-6 


43-1 


45-6 




3i 


27-5 


30-2 


33-0 


35-7 


38-5 


41-3 


43-9 


46-7 


49-4 




3d 


29-6 


32-5 


35-5 


38-5 


41-4 


44-4 


47-3 


50-3 


53-2 




35 


31-7 


34-9 


38-0 


41-2 


44-4 


47-5 


50 7 


53-9 


57-0 




4 


33-8 


37-2 


40-6 


43-9 


47-3 


50-7 


54-1 


57-5 


60-8 




4i 


35-9 


39-5 


43-1 


46-7 


50-3 


53-9 


57-5 


61-0 


64-6 




44 


;>8-o 


41-8 


45-6 


49-4 


53-2 


57-0 


60-8 


64-6 


68-4 




4| 


40-1 


44-1 


48-2 


52-2 


56-2 


60-2 


64-2 


68-2 


72-2 




5 


42-2 


48-5 


50-7 


54-9 


59-1 


63-4 


65-6 


71-8 


76-0 




5i 


44-4 


48-8 


53-2 


57-7 


62-1 


66-5 


71-0 


75-4 


79-9 




•5i 


4G-5 


51-1 


55-8 


60-4 


65-1 


69-7 


74-4 


79-0 


83-C 




51 


48-6 


53-4 


58-3 


63-2 


68-0 


72-9 


77-7 


82-6 


87-5 


1 


6 


50-7 


55-8 


60-8 


65-9 


70-9 


76-0 


81-1 


86-2 


91-2 


8 
I 
I 
1 


1 

u 
1* 


12-7 


13-9 


15-2 


16-5 


17-7 


19-0 


20-3 


21-5 


22-8 


15-8 


17-4 


19-0 


20-6 


22-2 


23-8 


25-3 


28-9 


28-5 


19-0 


20-9 


22-8 


24-7 


26-6 


28-5 


30-4 


32-3 


34-2 


22-2 


24-4 


26-6 


28-8 


31-1 


33-3 


35-5 


37-7 


39-9! 


l 

1 1 
1 


2 


25-3 


27-9 


30-4 


33-0 


35-5 


38-0 


40-6 


43-1 


45-6 


2| 
2£ 


28-5 


31-4 


34-2 


37-1 


39-9 


42-8 


45-6 


48-5 


51-31 


31-7 


34-9 


38-0 


41-2 


44-4 


47-5 


50-7 


53-9 


57-0 1 



11* 



121 




| 

PRACTICAL TABLES. 




TABLE /II.-FLAT IRON. 




Th'k. 


WwL 


1ft 2ft 

1 


3ft 


4ft 


5ft 


6ft 


7ft 


8ft 


9ft 




inch. 


inch. 


lbs. lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 




§ 


21 


3-5; 7-0 


10-5 


13-9 


17-4 


20-9 


24-4 


27-9 


31-4 






I 


3 


. 1 

3-8 7-6 


11-4 


15 2 


19-0 


22-8 


26-6 


30-4 


31-2 






1 


3| 


4-1 8-2 


12-4 


16-5 


20-6 


24-7 


28-8 


33-0 


371 






I 


3£ 


4-4 | 8-9 


13-3 


17-7 


22-2 


26-6 


31-1 


35-5 


39-9 






I 


31 


4-8* 


9-5 


14-3 


19-0 


23-8 


28-5 


33-3 


38-0 


42-» 






§ 


4 


5-1 


10-1 


15-2 


20-3 


25-3 


30-4 


35-5 


40-6 


45-6 






1 


44 


5-4 10-8 


16-1 


21-5 


26-9 


32-3 


37-7 


43-1 


48-5 






1 


4£ 


5-7 11-4 


17-1 


22-8 


28-5 


34-2 


39-9 


45-6 


51-3 


1 




I 


4| 


6-0' 12-0 

1 


18-1 


24-1 


30-1 


3i>l 


42-1 


48-2 


54-2 






I 


5 


6-3 12-7 


19-0 


25-3 


31-7 


38-0 


44-4 


50-7 


57-0 






f 


54 


6-7 13-3 


20'0 


26-6 


33-3 


39-9 


46-6 


53-2 


59-9 






1 


H 


7-0 13-9 


20-9 


27-9 


34-9 


41-8 


48-8 


55-8 


62-7 






§ 


5| 


7-3 14-6 

1 


21-9 


29-2 


36-4 


43-7 


51-0 


58-3 


65-6 






I 


6 


7-6 15-2 


22-8 


30-4 


38-0 


45-6 


53-2 


60-8 


G8 I 






h 


1 


1-7 3-4 


5-1 


6-8 


8-5 


10-1 


11-8 


13-5 


15-2 






h 


14 


2-1 4-2 


6-3 


8-4 


10-6 


12-7 


14-8 


16-9 


190 






i 


u 


2-5 5-1 


7-6 


10-1 


12-7 


15-2 


17-7 


20-3 


22-8 






h 


n 


3-0 5-9 

| 


8-9 


11-8 


14-8 


17-7 


20-7 


23-7 


2G-6 






I 


2 


3-4 6-8 


10-1 


13-5 


16-9 


20-3 


23-7 


27-0 


30-4 






i 


24 


3-8 7 6 


11-4 


15-2 


19-0 


22-8 


26-6 


30-4 


34-2 






* 


s» 


4-2 8-4 


12-7 


16-9 


21-1 


25-3 


29-6 


33-8 


38-0 






i 


21 


4-6 


9-3 


13-9 


18-6 


23-2 


27-9 


32-5 


37-2 


41-8 






4 


3 


5-1 


10-1 


15-2 


20-3 


25-3 


30-4 


35-5 


40-6 


45-6 






4 


34 


5-5 11-0 


16-5 


22-0 


27-5 


32-9 


38-4 


43-9 


49-4 






£ 


3i 


5-9 11-8 


17-7 


23-7 


29-6 


35-5 


41-4 


47-3 


534 






4 


31 


6-3 12-7 

| 


19-0 


25-3 


31-7 


38-0 


44-4 


50-7 


57-0 






i 


4 


6-8 ' 13-5 


20-3 


27 


33-8 


40-6 


47-3 


54-1 


fiO-8 





PRACTICAL TABLES. 



125 



TABLE III FLAT IRON. 



Th'k. 

inch 
I 



Wid. 



inch 

21 

3 

31 
34 
31 

4 

4| 
44 
41 

5 

5i 

54 
55 



1 

n 
u 

n 

2 
2| 
24 
21 

3 

3* 
34 
31 



10ft lift 12ft 



lbs. 
34-9 

38-0 
41-2 
44-4 
47-5 



50-7 55 



53-9 
57-0 
60-2 

63-3 
66-5 
69' 
72-9 

76-0 

16-9 
21-1 
25-3 
2J-6 

33-8 
38-0 
42-2 
46-5 



59-2 
63-3 



lbs 
36-3 

41-8 
45-3 
48-8 
52-3 



59-3 
62-7 
66-2 72-2 



G9-7 
73-2 

76-7 
80-2 

83-f 

18-( 
23-2 
27-9 

3 

37-2 

41-8 
4G-5 
51-1 



50-7 55-8 
54-9 00-4 



65-1 
C9-7 



lbs. 
41-8 

45-6 
49-4 
53-2 
57-0 

60-8 
64-7 
68-4 



13ft 



76-0 
79-8 
83-7 
87-5 

91-2 

20-3 
25-3 
30-4 
35-5 

40-6 
45-6 
50-7 
55-8 

60-8 
65-9 
710 
76-0 



lbs. 
45-3 

49-4 
53-6 
57-7 
61-8 



65-9 70 



70-0 
74-2 
78-3 

82-4 
86-5 
9CV 
91-7 

98-9 

22-0 
27-5 
33-0 
38-5 

43-9 
49-4 
54-9 

60-4 

65-9 
71-4 

76-9 
83-4 



14ft 



lbs, 

48-8 

53-2 
57-7 
62-1 
66-5 



75-4 
79-9 
84-3 

88-7 
93-1 
97-6 
102-0 

L06-5 

23-7 
29-6 
35-5 
41-4 

47-3 
53-2 
59-1 
65-1 

70-9 

7o-9 
82-8 

88-7 



15ft lGi't 



67-6| 74-4 84-1 1 87-9 94-6 101-4 108-2 114-9 121-7 



lbs. 
52-3 

57-0 
61-8 
66-5 
71-3 

7G-0 
80-8 
85 

90-3 

95-0 
99-8 
104-5 
109-3 

114-1 

25-4 
31-7 
38-0 
44-4 

50-7 
57-0 
63-4 
G9-7 

7G-0 
82-4 

88-7 
95-0 



lbs. 
55-8 

60-8 
65-9 
71-0 
76-0 

81-1 
86-2 
91-3 
96-3 



17 A 18ft! 



lbs. 
59-3 

G4-6 
70-0 
75-4 



86-2 
91-6 
97-0 
102-3 



101-4 107-7 
106-5 113-1 



111-5 
116-6 

121-7 

27-0 
33-8 
40-6 
47-3 

54-1 
60-8 
65-6 
74-4 

81-1 
87-9 
94-6 
101-4 



118-5 
123' 

129-3 

28-7 
35-9 
43-1 
50-3 

57-5 
64-6 
71-8 
79-0 



93-3 
100-6 
107-7 



lbs. 



68-4 
74 
79 9 
85-5 

91-2 
97-0 
102-7 
108-4 

114-0 
119-8 
125-5 
131-2 

136-9 

30-4 
38-0 
45 
53-2 

60-8 
68-4 
76-0 
83-6 

91-2 

98-8 
106-5 
114-0 



/__ 

i26 




ritAOTICAL TABLES. 










'ABLE III. — FLAT IRON 






Th'k. 


Wid 


1ft 


2 ft 


3ft 


ft 5 


5 ft 


Gft 


7ft 


8ft 

lbs. 


9ft 

lbs. 


inch. 


inch. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 




h 


4* 


7-2 


14-4 


21-5 


•28-7 


35-9 


43-1 


50-3 


57 4 


646 






h 


44 


7-6 


15-2 


22-8 


30-4 


38-0 


45-6 


53-2 


60-8 


68 4 






h 


45 


8-0 


16-1 


24-1 


32-1 


40-1 


48-2 


56-2 


642 


722 






h 


5 


8-4 


16-9 


25-3 


33-8 


42-2 


50-7 


59-1 


676 


76-0 






h 


5* 


8-9 


17-7 


26-6 


35-5 


44-4 


53-2 


62-1 


71-0 


79-9 






h 


54 


9-3 


18-6 


27-9 


37-2 


4G-5 


55-8 


65-1 


74-4 


83-7 






i 


5| 


9-7 


19-4 


29-2 


38-9 


48-6 


58-3 


68-0 


77-7 


87-5 






h 


6 


10-1 


20-3 


30-4 


40-6 


50-7 


60.8 


70-9 


81-1 


91-2 






& 


1 


2-1 


4-2 


6-3 


8-4 


10-6 


12-7 


14-8 


16-9 


19-0 






§ 


H 


2*6 


5-3 


7-9 


10-6 


13-2 


15-8 


18-5 


21-1 


23-8 






I 


14 


3-2 


6-3 


9-5 


12-7 


15-8 


19-0 


22-2 


25-4 


28-5 






1 


If 


3-7 


7-4 


11-1 


14-8 


18-5 


22-2 


25-9 


29-6 


33-3 






| 


2 


4-2 


8-4 


12-7 


16-9 


211 


25-3 


29-9 


33-8 


38-0 






i 


2* 


4-8 


9-5 


14-3 


19-0 


23-8 


28-5 


33-3 


38-0 


42-8 






1 i 


24 


5-3 


10-6 


15-8 


2M 


26-4 


31-7 


37-0 


42-2 


47-5 






i 


21 


5-8 


11-6 


17-4 


23-2 


29-0 


34-8 


40-7 


46-5 


52-3 






§ 


3 


6-3 


12-7 


19-0 


25-3 


31-7 


38-0 


44-4 


50-7 


57-6 






I 


3| 


6-9 


13-7 


20-6 


27-5 


34-3 


41*2 


48-1 


54-9 


61-8 






8 


3£ 


7-4 


14-8 


22-2 


29-6 


37-0 


44-4 


51-8 


59-2 


66-5 






§ 


31 


7*9 


15-8 


23-8 


31-7 


39-6 


47-5 


55-5 


63-4 


71-3 






f 


4 


8-4 


16-9 


25-3 


33-8 


42-2 


50*7 


59-1 


67-6 


76-0 






f 


41 


9-t) 


18-0 


26-9 


35-9 


44-9 


53-9 


62-9 


7l-a 


80-8 






1 


44 


9-5 


19-0 


28-5 


38-0 


47-5 


57-0 


G6-5 


76-1 


8o-C 






1 


41 


lo-o 


20-1 


30-1 


40-1 


50-2 


60-2 


70-2 


80-3 


90-3 






I 


5 


.0-6 


21-1 


31-7 


42-3 


52-8 


63-4 


73-9 


84-5 


95-1 






t 


54 


j 1-1 


22-2 


33-3 


44-4 


55-5 


66-5 


77-6 


88-7 


99-8 






1 


54 


.1-6 


23-2 


34-9 


46-5 


58-1 


69-7 


81-3 


92-9 


104-6 






_J_ 


51 


12-1 


24-3 


35-4 


48-G 


60-7 


72-9 


85-0 


97-2 


109-3 















- 






















1 




PRACTIC/L TABLES. 12"/ 








TABLE III.— FLAT IRON 






Th'k. 


Wid. 


10ft 


lift 


12rt 


13ft 


14ft 


15ft 


l()ft 


17ft 


18ft 


inch. 


inch. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 




i 


4J 


71-8 


79-0 


86-2 


93-4 


100-5 


107-7 


111-9 


2»1 


129-3 






h 


44 


76-0 


83-6 


91-2 


98-9 


100-5 


114-1 


121-7 


129-3 


136-9 






4 


45 


80-3 


88-3 


96-3 


104-3 


112-4 


120-4 


128-4 


136-4 


144-5 






4 


5 


84-5 


92-9 


101-4 


109-8 


118-3 


126-7 


135-2 143-6 


152-1 






h 


5i 


88-7 


97-6 


106-5 


115-4 


124-2 


133- 1 


142-0 150-8 


159-7 






i 


54 


93-0 


102-2 


111-5 


120-8 


130-1 


139-4 


148-7 158-0 


167-3 






4 


51 


97-2 


100-9 


116-6 


126-3 


136-0 


145.8 


155-5 165-2 


174-9 






i 


6 


101-4 


111-5 


121-7 


131-8 


141-9 


152-1 


162-2 172-4 


182-5 






e 


1 


21-1 


23-2 


25-3 


27-5 


29-6 


31-7 


1 
33-fe | 35-9 


38-0 






i 


u 


26-4 


29-0 


31-7 


34-3 


37-0 


39-6 


42-21 44-9 


47-5 






i 


n 


31-7 


34-8 


38-0 


41-2 


44-4 


47-5 


50-7 


53-9 


57-0 






i 


n 


37-0 


40-7 


44-4 


48-1 


51-8 


55-5 


59-2 


62-8 


66-5 






i 


2 


42-2 


46-5 


50-7 


54 9 


60-1 


63-4 


67-6 


71-8 


76-0 






t 


»4 


47-5 


52-3 


57-0 


51-8 


66-5 


71-3 


76-0 


80-8 


85-5 






t 


24 


52-8 


58-1 


63-4 


68-6 


73-9 


79-2 


84-5 


89-8 


95-0 






i 


25 


58-1 


63-9 


69-7 


75-5 


81-3 


87-1 


92-9 


98-7 


104-5 






i 
i 


3 


63-3 


69-7 


76-0 


82-4 


88-7 


95-0 


101-4 


107-7 


114-0 






34 


68-7 


75-5 


82-4 


89-3 


96-1 


103-0 


109-9 116-7 


123-6 






i 


34 


73-9 


81-3 


88-7 


96-1 


103-5 


110-9 


118-3 125-7 


133-1 






8 


3! 


79-2 


87-1 


95-1 


103-0 


1109 


118-8 


126-8 134-7 


142-C 






§ 


4 


84-5 


92-9 


101-4 


109-8 


118-3 


120-7 


135-2 143-6 


1521 






1 


44 


89-8 


98-8 


107-8 


110-7 


125-7 


134-7 


143-7 152-6 


101 6 






| 


44 


95-1 


104-6 


H4-1 


123-6 


133-1 


142-6 


152-1 161-6 


171*1 






1 


4$ 


100-3 


110-4 


120-4 


130-4 


140-5 


150-5 


100-5 170-6 


180-6 


. 




1 


5 


105-6 


116-2 


126-8 


137-3 


147-9 


158-4 


169-0 179-6 


190-1 






1 


54 


110-9 


122-0 


133-1 


144-2 


155-3 


166-4 


177-5 188-5 


199-6 






1 


54 


116-2 127-8 139-4 


151-0 


162-6 


174-3 


185-9 197-5 


209-1 






1 1 


53 


121-5 133-0 1 115-7 157-9 170-0 182-2 


194-3 200-5 


218-6 




v- "- 











128 




j 

PRACTICAL TABLES. 






TABLE III. — FLAT IROJS 




Thk. 

inch 


Wid. 


1 ft! 2 ft 


3ft 


4 ftj 5 ft 6ft 


7ft 


8ft 


9 it 




inch. 


lbs. 


Iba. 


lbs. 


lbs. 


lbs. \ lbs. 


lbs. 


lbs. 


lte . 






1 


6 


12-7 


25-3 


38-0 


50-7 


63-4 76-0 


88-7 


101-4 


114-1 ' 




I 
1 
1 


1 


2-5 


5-1 


7-6 


10-1 


12-7 15-2 


17-7 


20-3 


22-8 






u 


3-2 


6-3 


9-5 


12-7 


15-8 19-0 


22-2 


25-4 


28-5 






14 


3-8 


7-6 


11-4 


15-2 


19-0 22-8 


26 6 


30-4 


24-2 






« 


4-4 


8-9 


13-3 


17-7 


22-2 26-6 

| 


31-1 


35-5 


39-9 






1 
I 
1 
1 


2 


5-1 


10-1 


15-2 


20-3 


1 
25-3 30-4 


35-5 


40-6 


45-6 






2| 


5-7 


11-4 


17-1 


22-8 


28-5 34-2 


39-9 


45-6 


51-3 






2i 


6-3 


12-7 


19-0 


25-3 


31-7! 38-0 


44-4 


50-7 


57 






2| 


7-0 


13-9 


20-9 


27-9 


34-9 1 41-8 

i 


48-8 


55-8 


62-7 






1 
1 
1 
1 


3 


7-6 


15-2 


22-8 


30-4 


38-0 45-6 


53-2 


60-9 


68-4 






3i 


8-2 


16-5 


24-7 


33-0 


41-2 49-4 


57-7 


65-9 


74-2 






3£ 


8-9 


17-7 


26-6 


35-5 


44-4 53-2 


62-1 


71-0 


79-9 






31 


9-5 


19-0 


28-5 


38-0 


47-5 


57-0 


66-5 


76-1 


85-6 






1 
1 
i 
i 


4 

44 

41 

41 


10- 1 


20-3 


304 


40-6 


50-7 


60-8 


70-9 


8M 


91-2 






10-8 


21-5 


32-3 


43-1 


53-9 


64-6 


75-4 


86-2 


97-0 






1J-4 


22-8 


34-2 


45-6 


57-0 


68-4 


79-9 


91-3 


102-7 






12-0 


24-1 


36-1 


48-2 60-2 


72-2 


84-3 


96-3 


108-4 






1 
1 
I 


5 


12-7 


25-3 


38-0 


50-7 1 63-4 76-0 


88-7 


101-4 


J14-0 






54 

54 


13-3 


26-6 


39-9 


53-2 66-5 79-8 


93-1 


106-5 


119-8 






13-9 


27-9 


41-8 


55-8 


69-7 


83-7 


97-6 


111-5 


125-5 






1 


51 


14-6 


29-1 


43-7 


58-3 


72-9 


87-4 


102-0 


116-6 


131-2 






I 


G 


15-2 


30-4 


45 6 


60-8 


76-0 


91-2 


10G-5 


1217 


136-9 




• 




u 


5-1 


10-1 


152 


20-3 


25-3 


30-4 


33-5 


40-6 


456 








2 


6-8 


13-5 


20-3 


27-0 


33-8 


40-6 


47-8 


54-1 


60-8 








3 


10-1 


20-3 


30-4 


40-6 


50-7 


60-8 


70-9 


81-1 


91-2 








4 


13-5 


270 


40-6 


64-1 


67-6 


81-1 


94-6 


108-1 


121-7 








5 


16-9 


33-8 


50-7 


67-6 


84-5 101-4 


118-3 


135-2 


152-1 




* 


6 


20-3 


40-6 


60 8 81-1 


101-4 121-7 


141-9 162-21182-5 









PRACTICAL TABLES. 12^ 






TABLE III. — PLAT IRON. 






Th'k. 


Wid. 


10ft 


lift 


12ft 


13ft 


14ft 


15ft 


IGft 


17ft 


18ft 




inch. 


inch. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 




8 


6 


126-7 


139-4 


152-1 


164-8 


177-4 


190-1 


202-8 


215-4 


228 1 






1 


1 


25-3 


27-9 


30-4 


33-0 


35-5 


38-0 


40-6 


43-1 


45-6 






i 


14 


31-7 


34-9 


38-0 


41-2 


44-4 


47-5 


50-7 


53-9 


57-0 






1 


38-0 


41-8 


45-6 


59-4 


53-2 


57-0 


60-8 


64-6 


. 68-4 






I 


H 


44-4 


48-8 


53-2 


57-7 


62-1 


66-5 


71-0 


75-4 


79-9 






1 
1 


2 


50-7 


55-8 


60-8 


65-9 


70-9 


76-0 


81-1 


86-2 


91-2 






24 


57-0 


62-7 


68-4 


74-2 


79-9 


85-5 


91-3 


97-0 


102-7 






1 


2£ 


63-3 


69-7 


76-0 


82-4 


88-7 


95-0 


101-4 


107-7 


114-0 






1 


21 


69-7 


76-7 


83-7 


90-6 


97-6 


104-5 


111-5 


118-5 


125-5 






1 
1 
1 


3 


76-0 


83-6 


91-2 


98-9 


106-5 


114-1 


121-7 


129-3 


136-9 






34 
34 


82-4 


90-6 


98-9 


107-1 


115-3 


123-6 


131-8 


140-0 


148-3 






88-7 


97-6 


106-5 


115-4 


124-2 


133-1 


142-0 


150-8 


159-7 






1 


31 


95-1 


104-6 


114-1 


123-6 


133-1 


142-6 


152-1 


161-6 


171-1 






I 


4 
44 

41 


101-4 


111-5 


121-7 


131-8 


141-9 


152-1 


162-2 


172-4 


182-5 






107-7 


118-5 


129-3 


140-1 


150-8 


161-6 


172-4 


183-2 


193-9 






1 


114-1 


125-5 


136-9 


148-3 


159-7 


171-1 


182-5 


193-9 


205-3 






1 


120-4 


132-4 


144-5 


156-5 


168-6 


180-6 


192-6 


204-7 


2167 






1 


5 


126-7 


139-4 


152-1 


164-8 


177-4 


190-1 


202-8 


215-4 


228-1 






54 
5£ 


133-1 


146-4 


159-7 


173-0 


186-3 


199-6 


212-9 


226-2 


239-5 






i 


139-4 


153-3 


167-3 


181-2 


195-2 


209-2 


223-1 


237-0 


250-9 






1 


51 


145-7 


160-3 


174-9 


189-5 


204-0 


218-6 


233-2 


24 7 -8 


269-3 






1 


f> 


152-1 


167-3 


182-5 


197-7 


212-9 


228-1 


243-3 


258-5 


273-7 






1 


u 


50-7 


55-8 


60-8 


65-9 


70-9 


76-0 


81-1 


86-2 


91-2 






1 


2 


67-6 


74-4 


81-1 


87-9 


94-6 


101-4 


108-1 


114-9 


121-7 






1 


3 


101-4 


111-5 


121-7 


131-7 


141-9 


152-1 


162-2 


172-4 


182-5 






1 


4 


135-2 


148-7 


162-2 


175-7 


189-3 


202-8 


216-7 


229-8 


243-3 


' 




1 


5 


169-0 


185-9 


202-8 


219-7 


230-6 


253-5 


270-4 


287-3 


304-2 


i 1 


6 


202-8 


.223-1 


243-3 '2G3-6 


283-9 


304-2 


324-4 


344-7 


365-0 



130 



PRACTICAL TABLE8. 



The tables are all calculated to the nearest tenih of 
a pound. To the weights of bars of Wrought Iron, ada 
T £ v th part for bars of Soft Steel 



and from the same 



T? 1 



Proportional Breadths for hexagonal or six-sidtd Nut* 
for Wrought- Iron Bolts. 



Dia. of bolts. 


Breadth of nuts. 


Dia. of bolts. 


Breadth of nuts 


f 


£ inch. 


H 


lj-£ inch. 


i 
2 


1 " 


H 


•2A " 


k 


H " 


if 


2f " 


t 


ifV " 


H 


2tV '* 


I 


H " 


i| 


2J " 


1 


n - 


•f 


3 



Mote, — The thickness of the nut is equal the bolt's diaro 



WEIGHTS OF IRON, COPTER, ETC. 



13' 







Thickness in 


parts of an inch. 






ccj-^ifHco 


$>■&»**•&« 


"!« 3°'*+- 3" 


^05| U| 


3 

a 


*. co 

o in 


GO 

s 


!3 8 IS § 5 

0» ew en 


5» to © -i 

Cn cn 


cn to 
cn 








Thickness by the wire gauge. 






Cn A. 


CO 


5 w O O 00 


*j si cn *. 


co to 


M 


22 

p 


tO w 

% "to 


co 
cn 


*. cn cn oa o 
co cS to db 

oo » A o 


-j oo oo © 
cn -^ -J 
to A. 


£ to 


Cn 


3 

3 


to CO 
tg d> 


1 


en en at m «-i 

6 A t!i » 6 
oo 


qo to o *? 
«4 *» i— 6S 


to CO 
--I to 
cn 


4k 

cn 


o 

o 


co w 


<o 


.*». Cn 35 Oi -J 


11 

9-61 
8-93 

8-25 


to co 
►^ to 


u 

in 


ea 

■ 

X 






Thickness by 


the wire gauge. 






HSS 


5 SSSS 


B W «5 m 

85 h- S to 


00 -»J 


5 


p 


<5« cn 

i ^ 


s 








to 


3 

3 


£ A 6 5 


JO i W -j 

Cn i. 


do ^ 

C5 00 


cn eS 

00 ■»> 


-o 






to to 

m cn 
Cn to 


to 

to 


o 

■§ 

1 


db to © ^- co 

CO tO *. 05 


& oS «J to 

Cn to 00 ^1 


6 e 

i 


-j 






to to 

© i. 




C3 
1 


•4 do «& h- to 

to oo to Co 


tb cn 6S db 
-vl ilk <D <3 



" 2 

o "1 

O CO 

O d 

2 * 

► 2 

P 

W ^ 

p. o 

> 2 

co 

~ O 

•_ "3 

O !> 

co O 



Note. — No. 1 wire gauge equal -j^ths of an inch. 
"4 " i " 

" 7 " j\ 

.< „ u | 

" 16 " tV 

*« 22 " jV " 

The preat variety of thicknesses into which copper 
is manufactured, cause in trade the weigh*, to be named 
whereby to determine the thickness required, the unit 
12 



.32 



COMPARATIVE WEIGHTS OF BODIES. 



being- tnat of a common sheet, so designated, viz., i feet 
by 2 feet, in lbs., thud. — 

A 70 lb. plate is y 3 ^ths of an inch in thickness. 

a ^ U u « I « u u u u 

" 23 u 

" nh « 

" 6 « 

The thickness of lead is also in common determined 
or understood by the weight ; the unit being that of a 
square or superficial foot ; thus : — 



1 

32- 



6 

11 

15 



3 



COMPARATIVE WEIGHTS OF DIFFERENT BODIES 



Bar iron being 1, 


Cast iron being 1. 


Cast iron = -95 


Bar iron = I 07 


Steel = 1-02 


Steel = 108 


Copper = 1-16 


Brass = 116 


Brass = 109 


Copper = 1-21 
Lead = 1-56 


Lead = 1-48 



J. Suppose 1 have an article of plate iron, the weight 
of which is 728 lbs., but want the same of copper, and 
of similar dimensions, what will be its weight? 
728 x 1-16 = 844-48 lbs. 
2. A model of dry pine, weighing 32£ lbs., and in 
which the iron for its construction forms no materia, 
portion of the weight, what may I anticipate its weight 
to be in cast iron ? 

32-5 x 16 = 520 lbs. 
Ncte. — It frequently occurs, in the formation or construc- 
tion of models, that neither the quality nor condition of the 
timber can be properly estimated; and, in such cases, it may 
be a near enough .ipproximation to reckon 15 lbs. of cast iroi 
£> each lb. of model. 



COPPER PIPES, ETC 



135 



TO ASCERTAIN THE WEIGHTS OF PIPES OF 

VARIOUS METALS, AND ANY DIAMETER 

REQUIRED. 



Thickness 
; in parts of 
' an inch. 


Wrought 
iron. 


( 


opper. 


Lead. 


A 


•3*26 


1!£ lb* 


plate, -38 


2 


lbs. lead, -483 


tV 


•653 


23£ « 


•76 


4 


" " -9G7 


3 
? 2" 


•976 


35 " 


« 114 


5* 


u a j-45 


i 


IS 


46£ " 


« I -52 


8 


" " 1-933 


& 


1627 


53 « 


" 1-9 


9j 


u u 2-417 


t\ 


1-95 


70 « 


" 2-23 


11 


u u 2-9 


i? 


2-277 


80£ « 


" 2-66 


13 


« " 3-383 


i 


2-6 


93 " 


" 3-04 


15 


« « 3-867 



/ftf/e. — To the interior diameter of the pipe, in 
inches, add the thickness of the metal ; multiply the 
Bum by the decimal numbers opposite the required 
thickness, and under the metal's name; also, by the 
length of the pipe in feet; and the product is the 
-weight of the pipe in lbs. 

1. Required the weight of a copper pipe whose in- 
terior diameter is 74 inches, its length H{ feet, and the 
metal | of an inch in thickness. 

7-5 + -125 = 7-625 x 152 x 6-25 = 72-4 lbs. 

2. What is the weight of a leaden pipe 184 feet in 
length, 3 inches interior diameter, and the metal i of 
an inch in thickness ? 



lb 





3 4- -25 = 3-25 x 3-867 X 18-5 = 


232-5 lbs. 


Vote. 


- Weiebt of a cubic inch of 








Lead 


equal 


•4103 




Copper, sheet 


** 


•3225 




Brass, do. 


<t 


•3037 




Iron, do. 


" 


•279 




Iron, cast 


a 


•263 




Tin, do. 


" 


•2636 




Zinc. do. 


u 


•26 




Water 


u 


03617 



134 



BALLS. 



WEIGHT OF CAST IRON BALLS. 



Diameter 


Weight 


in inches. 


in His. 


2 


MO 


H 


1-57 


% 


215 


3 


2-86 


3* 


3-72 


% 


4-71 


5-80 


S| 


7-26 


4 


8-81 


44 


10-57 


4.| 


12-55 


4| 


14-76 


5 


17-12 


5 h 


19 93 


4 


22-91 


4 


2618 



Diameter 


Weight 


in inches. 


in lbs. 


6 


29-72 


6J 


33-62 


6| 


37-80 


6$ 


42-35 


7 


47-21 


3 


52-47 


58-06 


7| 


64-09 


8 


70-49 


84 


77-32 


8| 


84-56 


8J 


92-24 


9 


100-39 


9 I 


108-98 


1 


11806 


n 


127-63 



Diameter 


Weight 


in inches. 


in lbs. 


10 


137-71 


1( H 


148-28 


inj 


159-40 


lot 


171-05 


n 


183-29 


114 


196 10 


"I 


209 13 


HI 


223-40 


12 


237-94 


12,4 
12| 


253- 13 


268-97 


m 


285-37 


13 


302-41 


134 


320-80 


338-81 


m 


357-93 



1. What will be the weight of a hollow ball or shell 
of cast iron, the external diameter being 9£, and in- 
ternal diameter 8i| inches ? 

Opposite 9A are 11806, and 
Opposite 8| are 92-24, subtract 

— 25-82 lbs., weight required. 

2. Requiring to remove a cast iron ball 37-8 lbs. id 
weight, and in diameter 6£ inches, and replace it by 
one of lead of an equal weight, what must be th<3 
diameter of the leaden ball ? 

Weight of lead to that of cast iron =1-56 (see Table, page 132 j 
6-53 

Then = 3 a/176 = 5t inches, the diameter. 

1-56 



TIMBER MEASURE. 



135 



tables by which to facilitate the men- 
suration OF TIMBER. 

1. Flat or Board Measure. 



Breadth | Area of a 
n inches. lineal tool. 



•0208 

•0417 

•0623 

•0834 

•1042 

•125 

•1459 

•1667 

•1875 

•2084 

•2292 

•25 

•2708 

•2916 

•3125 



Area ol a I j Breadth Area off 
lineal foot. I I in incites. lineal foot. 



•3334 

•3512 

•375 

•3958 

•4167 

•4375 

•4583 

•4792 

•5 

•5208 

•5416 

•5623 

•5833 

•6042 

•625 

•6458 



•6667 

•6875 

•7084 

•7292 

•75 

•7708 

•7917 

•8125 

•8331 

•8542 

•875 

•8959 

•9167 

•9375 

•9583 

•9792 



Application and Use of the Table. 

1. Required the number of square feet in a board ol 
flank 1G£ feet in length, and 91 inches in breadth. 

Opposite 9| is -8125 x 165 = 13-4 square feet. 

2. A board 1 foot 2$ inches in breadth, and 21 feet 
in length ; what is its superficial content in square feet ? 

Opposite 2| is -2292. to which add the 1 foot. 
Then 1-2292 x21 = 25-8 square feet. 

3. In a board 15£ inches at one end, 9 inches at the 
rther, and 14£ feet in length, how many square feet ? 



15-5+9 



% or I 0208 - } and 1-0208 x 14 5 = 14-8 sq. ft 

12* 



136 



TIMBER MEASURE. 



2. Cubic or Solid Measure. 



Mean 

I girth in 

inches. 



Cubic ft. 
in each 
lineal ft. 



•25 
•272 
•294 
•317 
•340 
•364 
•39 
•417 
•444 
•472 
•501 
•531 
•562 
•594 
•626 
•659 
•694 
•73 
•766 
•803 
•84 
•878 
•918 
•959 
1- 

1-042 
1-085 
1-12S 
1174 
1-219 
1-265 
1-313 



Mean 

k girth in 

inches. 



Cubic ft. 
in each 
lineal ft. 



1-361 
141 

1-46 
1-511 

1-562 

1-615 

1-668 

1-722 

1-777 

1-833 

1-89 

1-948 

2-006 

2-066 

2-126 

2-187 

2-25 

2-313 

2-376 

2-442 

2-506 

2-574 

2-64 

2-709 

2-777 

2-898 

2-917 

2-99 

3-062 

3136 

3-209 

3-285 



Mean j Cubic ft. 
[ girth in | in ea^ h 
inches, j lineal 't. 

3-362 "" 

3-438 

3-516 

3-598 

3-673 

3-754 

3B35 

3-917 

4- 

4-084 

4168 

4-254 

4-34 

4-428 

4-516 

4-605 

4694 

4-785 

4-876 

4-969 

5-062 

5158 

5-252 

5-348 

5-444 

5-542 

5-64 

574 

5-84 

5-941 

6044 

6- 146 



CAST METAL CYLINDERS. 



13) 



In the cubic estimation of timber, custom has estab- 
lished the rule of { the mean girth being the side oi 
the square considered as the cross sectional dimensions 
hence, multiply the number of cubic feet per lineo. 
foot, as in the Table of Cubic Measure, opposite the 
i girth, and the product is the solidity of the given 
dimensions in cubic feet. 

Suppose the mean i girth of a tree 211 inches, and 
its length 10 feet, what are its contents in cubic feet ? 

3- 136 X 16 = 50-176 cubic feet. 



CAST METAL CYLINDERS. 

The cylinders are solid, each 1 foot in length. 



Diam. 


Iron. 


Copper. 


Brass. 


Lead. 


inches. 


lbs. 


lbs. 


lbs. 


lbs. 


1 


2-5 


3-0 


2-9 


3-9 


2 


9-8 


12-0 


11-4 


155 


3 


221 


27-0 


25-8 


34-8 


4 


39-3 


47-9 


45-8 


Gl-9 


5 


61-4 


74-9 


71-6' 


90-7 


6 


88-4 


107-8 


103-0 


139-3 


7 


120-3 


146-8 


140-2 


189-6 


8 


157-1 


191-7 


183-2 


347-7 


9 


198-8 


242-7 


231-8 


313-4 


10 


245-4 


299-5 


286-2 


387-0 



CAST IRON PIPES. 



This table shows the weight of pipes 1 foot long, of 
bores from 1 inch to 12 inches in diameter, advancing 
by 4 °f an mc h 5 anu " °f thicknesses from i of an 
inch to 1| inches, advancing by $ of an inch. 



138 




CAST IRON PIPES. 




I 

! 


bore. 


1 


1 


h 


| 


5 


I 


1 


U 


U 




la. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 




1 


31 


5-1 


7-4 


10-0 


12-9 


16-1 


19-6 


23-5 


27-6 






11 


3-7 


6-0 


8-6 


11-5 


14-7 


18-3 


22-1 


26-2 


30-7 






ll 


4-3 


6-9 


9-8 


13-0 


16-6 


20-4 


24-5 


29-0 


33-7 






n 


4-9 


7-8 


11-1 


14-6 


18-4 


22-6 


27-0 


3J-8 


36-8 






2 


5-5 


8-8 


12-3 


KM 


20-3 


24-7 


29-5 


34-5 


39-9 






2* 
2.| 


6-1 


9-7 


13-5 


17-6 


22-1 


26-8 


31-9 


37-3 


43-0 






6-7 


10-6 


14-7 


19-2 


23-9 


28-9 


34-4 


40-0 


46-0 






2] 


7-4 


11-5 


16-0 


20-7 


25-7 


31-1 


36-8 


42-8 


49-1 






3 


8-0 


12-4 


17-2 


22-2 


27-6 


33-3 


39-3 


45-6 


52-2 






3 1 


8-6 


12-3 


18-4 


23-8 


29-5 


35-4 


41-7 


48-3 


55-2 






3* 


9-2 


14-2 


19-6 


25-3 


31-3 


37-6 


44-2 


51-1 


58-3 






? 


9-8 


15-2 


20-9 


26-9 


33-1 


39-7 


46-6 


53-8 


61-4 






10-4 


16-1 


22-1 


28-4 


35-0 


41-9 


49-1 


56-6 


64-4 






11 


11-1 


17-1 


23-4 


30-0 


36-9 


44-1 


51 -G 


59-4 


67-6 






11-7 


18-0 


24-5 


31-4 


38-7 


4fi-2 


54-0 


62-1 


70-6 






41 


12-3 


18-9 


2fv8 


33-0 


40-5 


48-3 


5G-5 


64-9 


73-6 






5 


12-9 


19-8 


27-0 


34-5 


42-3 


50-5 


58-9 


67-6 


76-7 






II 


13-5 


20-7 


28-2 


36-1 


44-2 


52-G 


61-4 


70-4 


79-8 






14-1 


2 J -6 


29-5 


37-6 


40-0 


54-8 


63-8 


73-2 


82-8 






5J 


14-7 


22-6 


30-7 


39-1 


47-9 


56-9 


Gli-3 


76-0 


85-9 






6 


15-3 


23-5 


31-9 


40-7 


49-7 


59-1 


(18-7 


78-7 


88-8 






61 


lti-0 


24-4 


33-1 


42-2 


51-5 


Gl-2 


71-2 


81-2 


92-0 






4 


16-6 


25-3 


34-4 


43-7 


53-4 


63-4 


73-4 


84-2 


95-1 






6| 


17-2 


2(1-2 


35-6 


45-3 


55-2 


65-3 


76-1 


87-0 


98-2 






7 4 


17-8 


27-2 


30-8 


46-8 


56-8 


67-7 


78-5 


89-7 


101-2 






71 


18-4 


28-1 


38-1 


48-1 


58-9 


69-8 


81-0 


92-5 


104-2 






7| 


19-0 


29-0 


39-1 


49-9 


00-7 


72-0 


83-5 


95-3 


107 4 






7| 


19-6 


29-7 


40-5 


5J-4 


62-6 


74-1 


85-9 


98-0 


110-5 






8 


20-0 


30-8 


41-7 


52-9 


f.4-4 


76-2 


88-4 


100-8 


113-5 






*1 


20-9 


31-7 


43-0 


54-5 


G6-3 


78-4 


90-8 


103-5 


116-6 






8| 


21-7 


32-9 


44-4 


56-2 


68-3 


80-8 


93-5 


106-5 


119-9 






8 


22-1 


33-6 


45-4 


57-5 


70-0 


82-7 


95-7 


109-1 


122-7 






9 


22-7 


34-5 


4G-0 


59-1 


71-8 


84-8 


98-2 


111-8 


125-8 






9j 


23-3 


35-4 


47-9 


60-6 


73-6 


87-0 


100-6 


114-6 


128-9 






9J 


23-9 


3H-4 


49-1 


62-1 


75-5 


69-1 


103-1 


117-4 


131-9 






§4-5 


37-3 


50-3 


63-7 


77-3 


91-3 


105-5 


120-1 


1350 






10* 


25-2 


38-2 


51-5 


65-2 


79-2 


93-4 


108-0 


122-8 


138-1 






iov 


25-8 


39-1 


52-8 


06-7 


81-0 


95-6 


110-4 


125-6 


141-1 






10J 


26-4 


40-0 


54-0 


68-3 


82-8 


97-7 


112-9 


128-4 


144-2 






103 


27-0 


41-0 


55-2 


69-8 


84-7 


99-9 


115-4 


1 131-2 


147-3 






11 


27-6 


41-9 


56-5 


71-3 


8(1-5 


102-0 


117-8 


i 133-9 


150-3 






111 


28-2 


428 


57-7 


72-9 


88-4 


104-2 


1 120-3 


1 136-7 


153-4 






ll| 


28-8 


43-7 


58-9 


74-4 


90-2 1 10(5-3 


122-7 


139-4 


156-4 






111 


29-5 


44-6 


fiO-1 


75-9 


i 92-0 108-5 


1 125-2 


142-2 


1 159-5 






2 


301 


45-6 


fil-4 1 77-5 ! 93-6 1 110-6 


I 127-6 


1450 1 162-6 




. 

























DEGREES OF HEAT. 139 

TABLE FOR COMPOSITIONS OF BRASS, &,C* 
3 parts copper, tin, 1 zinc, for yellow brass. 



2 


u 


" 1 « 


for Spelter. 


4 


it 


1 « 4 « 

« 1 « J « 
1 " " 


for lathe bushea. 


4 


u 


still harder. 


6 


" 


for bearings of shafts 


5 


" 


u , a ^ « 


for harder beann(rs. 


7 


« 


« i « o " 


fit for pulley blocks. 


8 


« 


1 " « 


fit for wheels. 


9 


u 


« 1 " " 


gun metal 



The effect of different degrees of heat on different 
•odies, according to Fahrenheit's scale, are shown 
Delow : — 

Degrees 

Cast iron thoroughly melted, 20577 

Cast iron begins to melt, 17977 

Greatest heat of a common smith's forge, . . . 173127 

Flint glass furnace, strongest heat, 15897 

Welding heat of iron, greatest, 13427 

Swedish copper melts, .......... 4587 

Brass melts, 3807 

Iron red-hot in the twilight, 884 

Heat of a common fire, 790 

Iron bright red in the dark, 752 

Zinc melts, 700 

Mercury boils, 672 

Lead melts, £94 

The surface of polished steel becomes uniformly a 

deep blue, 58C 

The surface of polished steel becomes a pale straw 

color, • 460 

A mixture of 3 tin and 2 lead melts 332 



CENTRE, 



in a general sense, denotes a point equally remote 
from the extremes of a line, surface, or solid. 



140 CENTRES. 



CENTRE OF ATTRACTION 

Of a body, is that point into which, if all its rnattci 
is collected, its action upon any remote particle would 
still be the same. 



CENTRE OF EQUILIBRIUM 

Is the same, in respect to bodies immersed in a fluid 
as the centre of gravity is to bodies in free space. 

CENTRE OF FRICTION 

Is that point in the base of a body on which it re- 
volves, into which, if the whole surface of the base 
and the mass of the body were collected, and made to 
revolve about the centre of the base of the given body, 
the angular velocity destroyed by its friction would be 
equal to the angular velocity destroyed in the given 
body by its friction in the same time. 

CENTRE OF GRAVITY 

Of any body, or system of bodies, is that point upon 
which the body, or system of bodies, acted upon only 
by the force of gravity, will balance itself in all posi- 
tions ; hence it follows, that, if a line or plane, passing 
through the centre of gravity, be supported, the bodv 
or system will be also supported. 

CINTRE OF GYRATION 

Is that point into which, if the whole mass were 
collected, a given force, applied at a given distance, 
would produce the same angular velocity in the same 
time as if the bodies were disposed at their respective 
distances. 

This point differs from the Centre of Oscillation only 
n this, that, in the latter case, the motion is produced 



: 



COHESION. 141 

by the gravity of the body ; but, in the former, the body 
is put in motion by some other force, acting at one 
place only. 

COHESION 

Is that species of attraction which, uniting particle 
to particle, retains together th ; component parts of the 
same mass ; being thus distin .'lushed from adhesion, or 
that specios of attraction which takes place between 
the surfaces of similar or dissimilar bodies. The 
absolute cohesion of solids is measured by the force 
necessary to pull them asundei. Thus, if a rod of iron 
be suspended in a vertical position, having weight 
attached to its lower extremity till the rod breaks, the 
whole weight attached to the rod, at the time of frac- 
ture, will be the measure of its cohesive force, or abso- 
lute cohesion. 

The particles of solid bodies, in their natural state, 
are arranged in such a manner, that they are in equi- 
librium in respect to the forces which operate on them; 
therefore, when any new force is applied, it is evident 
that the equilibrium will be destroyed, and that the 
particles will move among themselves till it be restored. 
When the new force is applied to pull the body asunder 
the body becomes longer in the direction of the force, 
which is called the extension ; and its area, at right 
angles to the direction of the force, contracts. When 
the force is applied to compress the body, it becomes 
shorter in the direction of the force, which is called the 
compression ; and the area of its section, at right angles 
to the force, expands. In either case, a part of the 
heat, or any fluid that occupies the pores or interstices 
of the body, before the new force was made to act 
upon it, will be expelled. 



CASE-HARDENING. 



The hardness and polish of steel may be united, in 
ft certain degree, with the firmness and cheapness of 



142 



CASE-HARDENING. 



malleable iron, by what is called case-hardening; an 
operation much practised, and of considerable use. 

It is a superficial conversion of iron into steel, and 
only differs from cementation in being carried on for a 
shorter time. Some artists pretend to great secrets in 
the practice of this art, using saltpetre, sal-ammcniac 
and other fanciful ingredients, to which they attribute 
their success. But it is now an established fact, that 
the greatest effect may be produced by a perfectly 
tight box, and animal carbon alone. 

The goods intended to be case-hardened, being pre- 
viously finished, with the exception of polishing, are 
stratified with animal carbon, and the box containing 
them luted with equal parts of sand and clay. They 
are then placed in the fire, and kept at a light red heat 
for half an hour, when the contents of the box are 
emptied into water. Delicate articles, like files, may 
be preserved by a saturated solution of common salt, 
with any vegetable mucilage, to give it a pulpy con- 
sistence. The carbon here spoken of is nothing more 
than any animal matter, such as horns, hoofs, skins, or 
leather, just sufficiently burned to admit of being re- 
duced to powder. The box is commonly made of iron, 
but the use of it, for occasional case-hardening upon a 
small scale, may easily be dispensed with, as it will 
answer the same end to envelop the articles with the 
composition above directed to be used as a lute, drying 
it gradually before it is exposed to a red heat, other- 
wise it will probably crack. It is easy to infer, that 
the depth of the steel, induced by case-hardening, will 
vary with the time the operation is continued. It may 
be varied from one hour to four, according to the depth 
of steel required. In one hour, it will scarcely be the 
thickness of a fourpence, and therefore may be re- 
moved by violent abrasion, though sufficient to answer 
.veil for fire-irons, and a multitude of other utensils, in 
the common usage of which its hardness prevents its 
being easily scratched, and its polish preserved by 
friction with so soft a material as leather. 



STEAM-ENGINES. 



143 



To estimate, by means of an indicator, t \e amount of 
tjf'edive power produced by a steam-engine. 

Rule. — Multiply the area of the piston in square 
inches by the average force of the steam in lbs., and by 
the velocity of the piston in feet per minute ; divide the 
product by 33,000, and T 7 n ths of the quotient equal the 
effective power. 

Ex. Suppose an engine with a cylinder of 37£ inches 
diameter, a stroke of 7 feet, and making 17 revolutions 
per minute, or 238 feet velocity, and the average indi- 
cated pressure of the steam 16-73 lbs. per square inch , 
required the effective power. 

Area = 1104-4687 inches x 16-73 lbs., x 238 fe et. 

33000 
133-26 X 7 

= 93-282 horses' power. 

10 



To determine the proper velocity for the piston of a 
steam-engine. 

Rule. — Multiply the logarithm of the nth part of the 
stroke at which the steam is cut off by 2-3, and to the 
product of which add -7. Multiply the sum by the dis- 
tance in feet the piston has travelled when the steam is 
cut off, and 120 times the square root of the product 
equal the proper velocity for the piston in feet per 
minute. 

Ex. Let the steam be cut oft in an 8-feet stroke 
when the piston has travelled ^th of the length ; re- 
quired its proper velocity. 



Logarithm of 4 = 0-60206 
Multiplied by 



2-3 



To which add 



1 -.'584738 
•7 



2-084738 

2 



V 4- 169476 = 204 x 120 - 245 feet, velocitv 
iq per minute 



144 



STEAM-ENGINE 5. 



Table of Approximate Velocities for the Pistons of Steam- 
Engines. 



Condensing En 


gines. 


Non-condensing Engines. 


Length 


Velocity in 


Number of 


Length 


Velocity in 


Number of 


of stroke 


feet per 


revolutions 


of stroke 


feet per 


revolutions 


1 in feet. 


minute. 


per min. j 


in feet. 


minute. 


per mm. 


2 


160 


40 


H 


186 


62 


H 


mk 


35 £ 


2 


200 


50 


3 


192 


32 


4 


2124 
2171 


424 


H 


203 


29 


3l»4 


4 


214 


26| 


3 


222 


37 


H 


220A 


24| 


34 


231 


33 


5 


230 


23 


4 


236 


294 


5i 


236^ 


214 


H 


243 


27 


6 


240 


20 


5 


2474 


244 


7 


245 


"i 


H 


253 


23 


8 


256 


16 


6 


264 


22 



Of the Parallel Motion in a Steam-Engine. 

When the power from the piston is communicated 
by means of a beam or lever moving upon an axis, the 
parallel motion becomes a very important portion of the 
machine ; for then it forms the link of connection, and 
by its properties renders the action of alternate circular 
motion, and reciprocating- vertical motion, mutually 
agreeable, thereby properly insuring to the piston rod 
a truly direct line to that of the cylinder; but to eifect 
this, the greatest degree of exactitude of the various 
parts is required, otherwise extra friction is created, and 
the effective powe- of the engine proportionately dimin- 
ished 



PARALLEL MOTIONS. 



145 



Vable by which to determine the various Distances of tlu 
Movable Points in a Parallel Motion. 



1 g 


c 


Sg 


1 




-l 


a 


i 


■S ■ 


£ 


« . 


8gj 


r 


£ 


J 2 


£ 

S c 


c£ 


!i' = 


| 


& 






1 


J! 




2 


2 




3 




31 


G 0', 




5 


6 0* 


j 


2', 


1 4i| 




3* 


3 3 




4 


5 P3 




51 


5 3 




2$ 


JO; 


a> 


3.i 


2 6| 


w 


4 j 


4 3 


« 


5.1 


4 6:1 




23 


6J 




33 


2 04 





4', 


3 tijf 


<s 


H 


3 11 




3 


4 


SO 


4 
4>. 


1 <••: 

1 25 


X 


44 
5 


2 11* 

2 53 





6 
6 1 , 


3 31 

2 103 










2 


3 1* 




4J| 


10.5 




5 -1 


2 o,l 




6* 


2 5g 


<0 


2| 
21 


2 3 

1 7>, 












j n 




63 


2 1 




3 
3 J 


5 4 

4 4 


«M 


i ii 






4 


6 3 




^1 


6 3.1 




3 


9 




3i 


3 U 




41 


5 33 




5-2 


5 6 




<*4 


o 53 


0> 

<82 


33 
4 


3 2J 
2 3 




4i 

43 


4 6 
3 9j 


1 


53 
6 


4 94 
4 2 







4 6 


V 


21 


3 4jj 
2 6 




4* 


1 9 


.» 


b 


3 2* 


_ 


61 


3 7| 




2^ 
3 

11 




4', 


1 4S 


OS 


&4 


2 8] 
2 fe3 
1 10 
i 6 


r 1 


6* 


3 11 


0) 


1 10J 
1 4 
11} 

73 




43 
5 


1 0< 
9| 




hi 

53 
6 




^ 


2 84 | 


w 


54 
53 
6 
81 


6 6J 
5 9' 
5 01 
4 5" 




3\ 

33 
4 


4 6] 
3 9 
3 03 




a 


5 Of 
4 9 




?! 


4 83 
3 71 




2.i 

23 

3 




4} 


2 6 


s 


5 


4 0° 


-w 


61 


3 10,1 


«J 


2 9 


*" 


4A 


2 


£ 


53 


? hi 


^ 


61} 


3 4 


& 


2 1 


r~ 


43 


1 7 


-«• 


54 


2 lOj 




7 


2 10| 




31 


1 6jj 




5 


1 3 


CT> 


S3 


2 5', 




7.1 


2 6 


m 


3* 




*i 


114 




b 


2 0^ 





? 

81 


6 8}. 
6 




«4 


9] 




34 

3} 


s n 

4 9{ 




43 
5 


5 9.1 
5 0" 






2? 


3 10 


5 31 




3 


3 




4 


4 


« 


Si 


4 3.1 


g 


61 


4 7j 


J 


31 


2 3? 


1 " 


4\ 


3 33 


V 


5V 


3 81 


<£ 


63 


4 1 ! 


A 


3' ; 


1 9* 


<2 


4", 


■2 8| 


*" 


53 


3 13 


Ct 


7 


3 6J 
3 13 




3} 


1 4} 


CO 


4f 


2 2! 


2 


6 


2 8 


"-' 


7' 




4 


1 




5 


1 9j 




6', 


2 3 




7 * 


2 8*; 




4} 


84 




5J 


1 5', 




6* 


1 10* 




?4 


« 4 .i 



146 LOGARITHMS. 



LOGARITHMS. 

Logarithms literally signify ratios of numbers ; hence 
Logarithmic Tables may be various, but those in com- 
mon use for the facilitating of arithmetical operations 
generally are of the following corresponding progres 
sions, viz. : — 

Arithmetical, 0, 1, 2, 3, &c, or series of logarithms. 
Geometrical, 1, 10, 100, 1000, &c, or ratio of numbers. 

And thus it may be perceived, that if the log. of J be 
J, the log. of any number less than 10 must consist 
wholly of decimals, because increasing by a decimal 
ratio. Again; if the log. of 100 be 2, the log. of any- 
intermediate number between 10 and 100 must be 1. 
with so many decimals annexed ; and in like manner, 
the log. of any intermediate number between 100 and 
1000, must be 2, with decimals annexed proportionally, 
as before. 



APPLICATION AND UTILITY OF COMMON LOGA- 
RITHMIC TABLES. 

The whole numbers of the series of logarithms, aa 
1, 2, 3, &c, are called the indices, or characteristics 
of the logarithm, and which must be added to the 
logarithm obtained by the Table, in proportion to the 
number of figures contained in the given sum. Thus, 
suppose the logarithm be reqdired for a sum of only two 
figures, the index is 1 ; if of three figures, the index is 2 
and if of four figures, the index is 3, &c. ; being always 
a number less by unity than the number of figures the 
given sum contains. 



LOGARITHMS. 147 

Ex. Tl?^ *ndex o\ 8 is 0, because it is less than 10 

The index of 80 U; I. because it is less than 100. 

The index of 800 iv 2, because it is less than 1000. 

The inde^ of 800l.' is 3, because it is less than 
0,000, &c. 

The index of a decimal is always the number which 
denotes the significant figure from the decimal point, 
tnd is marked with the sign, thus, — , to distinguish it 
frotn a whole number. 

Ex. The index cf -32549 is — 1, because the first sig- 
nificant figure is the first decimal. 

The index of -032541) is — 2, because the first signi- 
ficant figure is the second decimal. 

The index of -0032549 is — 3, because the first sig- 
nificant figure is the third decimal, &c, of any other 
sum. 

If the given sum for which the logarithm is required 
contains or consists of both integers and decimals, the 
index is determined by the integer part, without having 
any regard to the other. 

1. To find the logarithm of flit/ whole number undei 
100. 

Look for the number under N in the first page of 
any Logarithmic Table ; then immediately on the right 
of it is the logarithm required, with ts proper index. 
Thus the log. of <J4 is 1 -806 180, and the log. of 72 is 
1-857332. 

2. To find tlie logarithm of any number between 100 
ind 1000, or any sum not exceeding 4 figures. 

Find the first three figures in the left-hand column 
of the page under N, in which the number is situated, 
und the fourth figure, at the top or bottom of the 
page ; then the logarithm directly under the fourth 
figure, and in a line with the three figures in the column 
vn the 3ft, with its proper index, is the logarithm re- 
13* 



1 48 LOGARITHMS. 

quired. Thus, the log. of 450 is 2-653212 and the log 
of 7464 is 3-872972. Or, the log. of 378-5 is 2-57806^ 
and that of -7854 is — 1-895091. 



3. To find the number indicated by a given logarithm 

Look for the decimal part of the given logarithm in 
the different col'imns, and if it cannot be found exactly, 
take the next less. Then under N in the left-hand 
column, and in a line with the logarithm found, arn 
three figures of the number required, and on the top oi 
the column in which the found logarithm stands is one 
figure more; place the decimal point as indicated by 
the logarithmic index, which determines the sum, prop- 
erly valued, as required. 

If the logarithm cannot be found exactly ir. the 
Tables, subtract from it trie next less that can be found, 
and divide the remainder by the tabular difference ; the 
quotient will be the rest of the figures of the given 
number, which, being annexed to the tabular number 
already found, is the proper number required. 

Ex. Required the number answering to ihe loga- 
rithm 3-233568. 

Given logarithm . . . . = 3-2335G8 
Next less is the log. of 1712 = 3-233504 

Remainder G4 

64 
Tab. r>;<r = 253, and — = -25 

253 
Hence the number required =1712-25. 

For practical purposes in mechanics, logarithms are 
seldom resorted to, unless for the raising of the powers 
of numbers or extraction of their roots. These opera- 
tions, M-hen tables are at hand, they very much facili- 
tate ; involution, or the raising of powers, being per- 
formed simply by multiplication, and evolution, or th« 
extraction of rooto, by division, as in simple arithmetic 



LOGARITHMS 149 

Ex. 1. Required the square or second power of 
25791. 

Log. of 25-791 = 1-411468 

Multiplied by 2 the power required. 

Logarithm 2-822936 indicated number or square re« 
quired = 665-175. 

Ex. 2. What is the cube of 307146? 

Logarithm = 1487345 

Multiplied by 3 the power required. 

Logarithm 4-462035 indicated number or cube required 
= 28975-7. 

Ex. 3. Required the square root of 3G5. 

2-562293 

Log. = — = 1 •283146 indicated number or root = 19-105. 

2 

Ex. 4. Find the cube root of 12345. 

4091491 
Log. = = 1-363830 indi-at^ «mmber or root = Mil lb 



1 1 

50 


LOGARITHMS. 








Table of Logarithms J rom 1 to 100 








N. 
1 


Log. 


N. 


Log. 


N. 


Log. 


N. 


Log. 


0-000000 


26 


1-414973 


51 


1-707570 


16 


1-380814 




n 


0-301030 


27 


1-431364 


52 


1-716003 


W 


1-886491 






3 


0-477121 


28 


1-447158 


53 


1-724276 


73 


1-892095 






4 


0-602060 


29 


1-462398 


54 


1-732394 


79 


1-897627 






5 


0-698970 


30 


1-477121 


55 


1-740363 


80 


^•903090 


• 


6 


0-778151 


31 


1 491362 


56 


1-748188 


81 


1-908485 




7 


0-845098 


32 


1-505150 


57 


1-755875 


82 


1-913814 






8 


0-903090 


33 


1-518514 


58 


1 763428 


83 


1-919078 






9 


0-954243 


34 


1-531479 


59 


1-770852 


84 


1-924279 






10 


1-000000 


35 


1-544068 


60 


1-778151 


85 


1-929419 




11 


1-041393 


36 


1-556303 


61 


1-785330 


86 


1-934498 




12 


1-079181 


37 


1-568202 


02 


1-792392 


87 


1-939519 






13 


1-113943 


38 


1-579784 


63 


1-799341 


88 


1-944483 






14 


1-146128 


39 


1-591065 


64 


1-80(5180 


89 


1-949390 






15 


1-176091 


40 


1-602060 


65 


1-812913 


90 


1-954243 




% 


16 


1-2041-20 


41 


1-612784 


66 


1-819544 


91 


1-959041 




17 


1-230449 


42 


1-623249 


67 


1-826075 


92 


1 -953788 






18 


1 255273 


43 


1-633468 


68 


1-832509 


93 


1-968483 






19 


1-278754 


44 


1-643453 


69 


1-838849 


94 


1-973128 






20 


1-301030 


45 


1-653213 


70 


1-815098 


95 


1-977724 




21 


1*322219 


46 


1-662758 


71 


1-851258 


96 


1-982271 




22 


1-342423 


47 


1-672098 


72 


1-857332 


97 


1-986772 






23 


1-361728 


48 


1-681241 


73 


1-863323 


98 


1-991226 






24 


1-380211 


49 


1-691 196 


74 


1-869232 


99 


1-995635 






25 


1-397940 


50 


1-698970 


75 


1-875061 


100 


2-000000 






No 


te. — The best Tables of Logarithms are those by Tayloi 


Gardi 


ner, Hutton, Babbage, and CailleL The smaller work 


f 


are t 


lose by Lalande, Hassler, Renaud, Christison, and WaJ 




lace,; 


ind those published in the " Library of Useful Knowfecge. 





WATER IN PIPES. 16 a 


TABLE WATER IN PIPES. 


This table shows the quantity and weight of watei 


tontained in one fathom of length of pipes of different 


Dores from 1 inch to 12 inches in diameter, advancing 


Dy half inch. The weight of a cubic foot of water is 


mken at 1000 ounces avoirdupois, and the imperial 


1 


gallon at 10 lbs. 






Diameter 


Quantity in 


Quantity in 


Weight in lbs 






in inches. 


cubic inches. 


imperial gallons. 
0-051 


avoirdupois. 




h 


1414 


0-51 




1 


56 55 


0-205 


2-05 






n 


127 23 


0-460 


4-60 






2 


22619 


0-818 


8-18 






2* 


353 43 


1-278 


12-78 






3 


508-94 


1-841 


18-41 






H 


692-72 


2-506 


25-06 






4 


904-78 


3272 


32-72 






4£ 


114511 


4- 142 


41-42 






5 


1413-72 


5113 


5113 






5£ 


1710-60 


6187 


61-87 






6 


2035-75 


7-363 


73-63 






6£ 


2389-18 


8-641 


86-41 






7 


2770-88 


10022 


100-22 






n 


3180-86 


11-505 


11505 






8 


361911 


13-090 


130-90 






8* 


4085-64 


14-777 


14777 






9 


4580-44 * 


16-567 


165 67 






9| 


5103-52 


18-459 


184-59 






10 


5654-87 


20-453 


204-53 






10£ 


623449 


22-550 


225-50 




11 


6842-39 


24-748 


247-48 






114 


7478-56 


27049 


270-49 






12 


814301 


29-452 


294-52 











52 CHANGES IN THE STRUCTURE OF IRON. 



CHANGES INDUCED IN THE STRUCTURE OF 
IRON SUBSEQUENT TO MANUFACTURE. 

The important purposes to which iron is applied have 
a.ways rendered it a subject of peculiar interest ; and 
at no period has its importance been so general and 
extensive as at the present time, when its application is 
almost daily extending, and there is scarcely any thing 
connected with the arts to which, either directly or 
indirectly, it does not in some degree contribute. My 
object is to point out some peculiarities in the habitudes 
of iron, which appear to have almost wholly escaped 
the attention of scientific men, and which, although in 
some degree known to practical mechanics, have been 
generally considered by them as isolated facts, and not 
regarded as the results of a general law. The circum- 
stances, however, well deserve the attention of scientific 
men, on account of the very important consequences to 
which they lead. 

The two great distinctions, which exist in malleable 
wrought iron, are known by the names of red-short and 
cold-short qualities. The former of these comprises 
the tough, fibrous iron, which generally possesses con- 
siderable strength when cold ; the latter shows a bright, 
crystallized fracture, and is very brittle when cold, but 
works ductile while hot These distinctions are per- 
fectly well known to all those who are conversant with 
the qualities of iron ; but it is not generally known that 
there are several ways by which the tough, red-short 
iron becomes rapidly converted into the crystallized ; 
and that, by this change, its strength is diminished to a 
very great extent. The importance which attaches to 
this subject will not be denied. The principal causes 
which produce this change are percussion, heat, and 
magnetism ; and it is doubtful whether either of these 
weans will produce this effect; and there appear strong 
reasons for supposing that, generally, they are all in 



CHANGES IN THE STRUCTURE OF IRON 153 

gome degree concerned in the production of the ob- 
served results. The most common exemplification or* 
the effect of heat, in crystallizing fibrous iron, is by 
breaking a wrought-iron furnace-bar; which, whatever 
quality it was of in the first instance, will, in a short 
time, invariably be converted into crystallized iron ; 
and, by heating, and rapidly cooling by quenching with 
water a few times, any piece of wrought iron, the same 
effect may be far more speedily produced. In these 
cases, we have at least two of the above causes in 
operation — heat and magnetism. In every instance 
of heating iron to a very high temperature, it under- 
goes a change in its electric or magnetic condition; 
for, at very high temperatures, iron entirely loses its 
magnetic powers, which return, as it giadually cools to 
a lower temperature. In the case of quenching the 
heated iron with water, we have a still more decisive 
assistance from the electric and magnetic forces ; for 
Sir Humphrey Davy long since pointed out, that ail 
cases of vaporization produced negative electricity in 
the bodies in contact with the vapor; — a fact which 
has lately excited a good deal of attention, in conse- 
quence of the discovery of large quantities of negative 
electricity in effluent steam. These results, however, 
are practically of but little consequence ; out the effects 
of percussion are at once various, extensive, and ot 
high importance. We shall trace these effects under 
several different circumstances. 

In the manufacture of some descriptions of ham- 
mered iron, the bar is first rolled into shape, and the« 
one-half the length of the bar is heated in a furnace, 
and immediately taken to the tilt-hammer and ham- 
mered ; and the other end of the bar is then heated 
and hammered in the same manner. In order to avoid 
any unevenness in the bar, or any difference in its 
color where the two distinct operations have terminated, 
the workman frequently gives the bar a few blows 
with the hammer on that part which he first operated 
upon. That part of the bar has, however, by this time, 



154 CHANGES IN THE STRUCTURE OF IRON. 

become comparatively cold ; and, if this cooling pro- 
cess has proceeded too far when it receives this addi- 
tional hammering, that part of the bar immediately 
becomes crystallized, and so extremely brittle that it 
will break to pieces by merely throwing it on the 
ground, though all the rest of the bar will exhibit the 
best and toughest quality imaginable. This change, 
therefore, has been produced by percussion as the 
primary agent We here see the effects of percussion 
in a very instructive form. And it must be observed, 
that it is not the excess of hammering which produces 
the effect, but the absence of a sufficient degree of 
heat at the time the hammering takes place ; and the 
evil may probably be all produced by five or six blows 
of the hammer, if the bar happens to be of a small 
size. In this case, we witness the combined effects of 
percussion, heat, and magnetism. When the bar is 
hammered at the proper temperature, no such crystal- 
lization takes place, because the bar is insensible to 
magnetism ; but, as soon as the bar becomes of that 
lower degree of temperature at which it can be affected 
by magnetism, the effect of the blows it receives is tc 
produce magnetic induction ; and that magnetic in- 
duction, and consequent polarity of its particles, when 
assisted by further vibrations from additional percussion, 
produces a crystallized texture. For it is perfectly 
weJl known that, in soft iron, magnetism can be almost 
instantaneously produced by percussion ; and it is 
probable that, the higher the temperature of the bar at 
the time it receives the magnetism, the more likely 
will it be to allow of that rearrangement of its mole- 
cules which would constitute the crystallization of the 
iron. It is not difficult to produce the same effects by 
repeated blows from a hand-hammer on small bars of 
iron; but it appears to depend upon something peculiai 
in the blow, which, to produce the effect, must occasion 
St complete vibration among the particles in the neigh 
Dorhood of the part which is struck. And it is re 
markable that the effects of the blows, in all cases 



CHANGES IN THE STRTJCTI RE OF IRON 156 

ieem to be confined within certain limited distances 
of the spot which receives the strokes. 

Dr. Wollaston first pointed out that the forms in 
which native iron is disposed to break, are those of 
the regular octahedron and tetrahedron, or rhomboid, 
consisting of these forms combined. The tough and 
fibrous character of wrought iron is entirely produced 
by art; and we see, in these changes that have been 
described, an effort at returning to the natural and 
primal form; — the crystalline structure, in fact, being 
the natural state of a large number of metals ; — and 
Sir Humphrey Davy has shown, that all those which 
are fusible by ordinary means assume the form of 
regular crystals by slow cooling. The general con- 
clusion, to which these remarks lead us, appears to 
leave no doubt that there is a constant tendency in 
wrought iron, under certain circumstances, to return to 
the crystallized state ; but that this crystallization is 
not necessarily dependent upon time for its develop- 
ment, but is determined solely by other circumstances, 
of which the principal is, undoubtedly, vibration. Heat, 
within certain limits, though greatly assisting the 
rapidity of the change, is certainly not essential to it 
but magnetism, induced either by percussion or other- 
wise, is an essential accompaniment of the phenomena 
attending the change. 



14 



156 STRENGTH OF JOURNALS OF SHAFTS, 



STRENGTH OF JOURNALS OF SHAFTS. 

Mr Buchanan's rule is — The cube root of the 
weignt in cwts. is nearly equal to the diameter of the 
journal ; — it being prudent to make the journal a little 
more than less, and to make a due allowance for wear- 
ing. 

Ex. What is the diameter of a journal of a water- 
wheel shaft, 13 feet long, the weight of the wheel being 
15 tons ? 

By Mr. B.'s rule, 

»V 15 X 20 = 6-7, or 7 inches diameter. 

By Mr. Tredgold's rule, 

3360 

Weight in the middle, X 13 = 873 3y873 = 9£ inches 

500 
diameter. 



Weight equally distributed, 33600 X 13 = 436800 ^^£2? 
= 7-65 inches. 



To resist Torsion or Twisting. 

It is obvious that the strength of revolving shafts* 
are directly as the cubes of their diameters and revolu- 
tions ; and inversely, as the resistance they have to 
evercome. 

Mr. Robertson Buchanan, in his essay on the Strength 
of Shafts, gives the following data, deduced from several 
experiments, viz. : That the fly-wheel shaft of a 50* 
horse-power engine, at 50 revolutions per minute, re- 
quires to be 7£ inches diameter ; and therefore, the cube 
of this diameter, which is — 421-875, seives as a multi- 

* Shafts, here, are understood as the journals of shafts, the Uciiet 
of shafts being generally made square. 



STRENGTH OF JOURNALS OF SHAFTS. 157 

plier to all other shafts in the same proportion ; and, 
taking this as a standard, he gives the following multi 
pliers, viz. : — 

For the shaft of a steam-engine, water-wheel, or any shaft 

connected with a first power, 400 

For shafts in inside of mills, to drive smaller machinery, or 

connected with the shafts above, 200 

For the small shafts of a mill or machinery, 100 

From the foregoing, the following rule is derived, 
viz. : The number of horses' power a shaft is equal to, 
is directly as the cube of the diameter and number of 
revolutions ; and inversely, as the above multipliers. 

Ex. 1. When the fly-wheel shaft of a 45-horse-power 
steam-engine makes 90 revolutions per minute, what is 
the diameter of the journal ? 

46x400 = 200 V200 = 5 T % inches diameter. 
90 

Ex. 2. The velocity of a shaft is 80 revolutions per 
minute, and its diameter is 3 inches ; what is its power ? 

33x80 K*V. 

=r 5-4 horses' power. 

400 

Ex. 3. What will be the diameter of the shaft in the 
first example, when used as a shaft of the second multi 
plier ? * 

5-8 . rA V i3 x i00 6 . , 

=s 404, or v = 4-^ inches diameter 

1-25 90 

The following is a table of the diameters of shalbs 
ucing the first movers, or having 400 for their multi- 
pliers. 

* The diameters of the second movers will be found by dividing th« 
numbers in the Table by 1*25, and the diameters of the third movers, 
»y dividing the numbers by 1-56. 



158 



DIAMETERS OF THE 



1 
N 

T 

5 
6 
7 
8 
9 

10 

12 

14 

16 

18 

20 

25 

30 

35 

40 

45 

50 

55 

60 


Revolutions. 


10 | 15 | 20 | 25 | 30 J 35 | 40 | 45 | 50 | 55 


Inches Diameter. 


5.5 

5-9 

6-3 

6-6 

6-9 

7-2 

7-4 

7-9 

8-3 

8-7 

9- 

9-3 

10- 

10-7 

11-4 

11-7 

12- 

126 

13-4 

136 


4-8 

51 

5-5 

5-8 

6- 

6-3 

6-6 

6-9 

7-2 

76 

7-9 

8-1 

8-5 

9-3 

9-8 

10-5 

10-6 

11- 

11 4 

12- 


4-5 
4-7 
5- 
5-2 
5-5 
5-7 
5-9 
6-3 
6-7 
71 
75 
7-7 
8- 
8-4 
8-9 
9-3 
9-7 
10- 
10-4 
10-8 


I 4 ' 
4-4 

4-6 

4-9 

51 

5-5 

5-6 

5-8 

6-2 

66 

7- 

7-2 

7-4 

7-9 

8-4 

8-8 

9-2 

9-3 

9-8 

10- 


37 
4 1 

4-4 

46 

4-8 

5- 

52 

5-6 

5-9 

6 1 

66 

6-8 

71 

7-4 

7-9 

8-3 

8-7 

9- 

91 

9-3 


3-8 
3-9 
4-1 
44 
46 
4-8 
4-9 
5-4 
5-6 
5-8 
62 
64 
6-8 
71 
7-4 
7-8 
8-1 
8-5 
8-8 
9- 


1 3-5 
37 
4- 
4 2 
4-4 
4-5 
4-7 
5-2 
5-4 
56 
5-8 
5-9 
6-3 
6-9 
7 1 
74 
7-6 
8- 
8-4 
8-6 


3-3 

36 

3-8 

4- 

4-2 

4-4 

46 

5- 

5-2 

5-4 

5-6 

5-7 

6- 

67 

6-9 

7-2 

7-4 

7-8 

8- 

8-2 


32 

3-5 

3-7 

3-9 

41 

4-2 

4-4 

4-8 

5- 

5-2 

5-4 

56 

5-9 

6-5 

66 

6-9 

7- 

7-4 

7-5 

7-7 


33 

36 

3-7 

4- 

41 

4-2 

4-6 

4-7 

5- 

5-2 

5-4 

5-6 

6-3 

6-5 

67 

6-8 

7-3 

7-4 

76 



JOURNALS OF FIRST MOVERS. 



159 





Revolutions. 


'?? 


60 | 65 | 70 | 75 | 80 | 85 | 90 | 95 | 100 | 105 


ill 

4 


Inches Diameter. 


3- 


2-9 


2-9 


2-8 


2-7 


27 


26 


2-6 


26 


2-5 


5 


3-3 


32 


31 


3- 


3- 


29 


2-9 


28 


2-8 


2-7 


6 


3-5 


35 


3-4 


33 


32 


32 


3- 


3- 


2-9 


2-9 


7 


36 


36 


3-5 


34 


34 


33 


3-3 


32 


31 


31 


8 


3-9 


3-8 


37 


3-6 


3-5 


35 


3-4 


3-4 


3 3 


32 


9 


4- 


3-8 


3-7 


3-7 


3-6 


3-6 


3-5 


3-5 


34 


3-3 


10 


4 1 


4- 


3-9 


3-8 


3-7 


37 


3-6 


3-6 


35 


34 


12 


44 


4-3 


42 


4 1 


4 


3-9 


3-8 


3-8 


3-7 


36 


14 
16 


4-5 

4-8 


4-4 

4-7 


44 
46 


4-3 
4-5 


4-2 
44 


4 1 

4-4 


4- 
43 


4- 

4-2 


3-9 


3-8 


41 


4- 


18 


5- 


49 


48 


4-7 


4-6 


45 


4 4 


4-3 


4-2 


4-2 


20 


52 


51 


5- 


4-8 


4-6 


4-6 


4-5 


4-5 


4-4 


4-4 


25 


5-5 


5-4 


5-3 


5-2 


51 


4-9 


4-8 


4-7 


4-6 


4-6 


30 


5-9 


5-8 


5-7 


56 


5-5 


5-3 


52 


51 


5- 


4-9 


35 


63 


61 


5-9 


5-7 


56 


5-5 


54 


5-3 


5-2 


5-2 


40 


6-6 


6-4 


6-2 


6- 


5-9 


5-8 


5-7 


5-6 


56 


5-5 


45 


6-7 


6-5 


64 


6-2 


61 


6 


5-9 


5-8 


5-7 


56 


50 


7-2 


69 


6-8 


66 


6-5 


64 


6-2 


6- 


5-9 


5-8 


55 


7-3 


72 


7- 


6-7 


66 


65 


6-3 


62 


61 


6- 


60 


7*4 


7 3 


72 


6-9 


6-8 


6-8 


67 


66 


6-4 


62 



14* 



160 STRENGTH OF WHEELS. 

It is a well known fact, that a cast iron rod will sns. 
tain more torsional pressure than a malleable iron rod 
of the same dimensions ; that is, a malleable iron rod 
will be twisted by a less weight than what is required 
to wrench a cast iron rod of the same dimensions. 

When the strength of malleable is less than that 
of cast iron to resist torsion, it is stronger than cast iron 
to resist lateral pressure, and that is in proportion as 9 
is to 14. 

From the foregoing, it is easy for the millwright tc 
make his shafts of the iron best suited to overcome the 
resistance to which they will be subject, and the pro- 
portion of the diameters of their journals, according to 
the iron of which they are made. 

Ex. What will be the diameter of a malleable iron 
journal to sustain an equal weight with a cast iron jour- 
nal of 7 inches diameter. 

73=343. 

M 14 : 343 : : 9 : 220£ ; now V 220 ' 5 = 604 inches diameter. 



STRENGTH OF WHEELS. 

The arms of wheels are as levers fixed at one end, 
and loaded at the other ; and, consequently, the greatest 
strain is upon the end of the arm next the axle. For that 
reason, all arms of wheels should be strongest at that 
part, and tapering toward the rim. 

The rule for the breadth and thickness of arms, ac- 
cording to their length and number in the wheel, is as 
follows : Multiply the power or weight acting at the end 
of the arm by the cube of its itength ; the product of 
which, divided by 2656 times the number of arms mul- 
tiplied by the deflection, will give the breadth, and 
cube of the depth. 

Ex. Suppose the force acting at the circumference 
of a spur-wheel to be 1600 lbs., the radius of wheel 6 



STRENGTH OF WHEELS. 



161 



feet, and number of arms 8, and let the deflection not 
exceed yVtfi of an inch. 

1600 x 63 



163 = breadth and cube of the depth 
163 



2656 X 8 x 

Let the breadth be 2-5 inches; therefore, — =65-2; 

2-5 

which is equal to the cube of the depth. Now the 
cube root of 65-2 is nearly 4-03 inches : this, conse- 
quently, is the depth or dimension of each arm in the 
direction of the force. 

Note. — When the depth at the rim is intended to be half 
that of the axes, use 1640 as a divisor instead of 2656. 

The teeth are as beams, or cantilevers, fixed at one end and 
loaded at the other. The rule applying directly to them where 
the length of the beam is the length of the teeth, and the depth 
the thickness of the teeth. For the better explanation of the 
rule, the following example is given. 

Ex. The greatest power acting at the pitch line ot 
the wheel is 6000 lbs., and the thickness of the teeth 
\h inch, the length of the teeth being 0-25 feet; it is 
required to determine the breadth of the teeth. 

6000 x 0-25 1500 „ . . , 

= = 3-2 inches, the breadth required. 

212 x.1-52 477 

In order that the teeth may he capable of offering a 
sufficient resistance after being worn by friction, the 
breadth thus fourd should be doubled ; therefore, ir the 
above example, the breadth should be 6-4, or say 6£ 
inches. 

The following data are gleaned from experiments, 
which are, therefore, valuable, and of much use to the 
practical mechanic. 

Rule. — Multiply the breadth of the teeth by the 
square of the thickness, and divide the product by the 
length ; the quotient will be the proportional strength 
in horses' power, with a velocity of 2-27 feet per second. 



162 



STRENGTH OF WHEELS. 



Ex. What is the power of a wheel, the teeth of 
which are 6 inches broad, ] 5 inch thick, and 1-8 inch 
ong, and revolving at the velocity of* 3 feet per second ' 

•i?2 x 6 J 3-5 

= =7-5, strength at 227 feet per second; then 

1-8 1-8 

2-27 : 7-5 : : 3 = 7 ' 5 x 3 - 9 91 horses' power. 

2-27 

Rule. — The pitch is found by multiplying the thick 
ness by 2-1, and the length is found by multiplying the 
thickness by 1*2. 

Ex. The thickness being 2 inches, what is the pitch 
tnd length ? 

2x2-1 = 4-2, pitch. 
2x 1-2 = 24, length 

Note. — The breadth of the teeth, as commonly executed by 
the best mechanics, seems to be from about twice to thrice the 
pitch. 











t. 


„ 


a 


c 


a 

09 . 

m m 


e 

to 


.5 • 


Ml 


<B 1) 

£ °- • 

2-12 


CDS 


JB 


M « 

u a 


■?s 


£c 








s 


2 

Eh 


« 


3" 


S3 CB 


O « 

a- «j 


SB a 


4-2 


2- 


8- 


2-40 


13-33 


17-61 


35-23 


3-99 


1-9 


7-6 


2-28 


1303 


15-90 


31-80 


3-78 


1-8 


7-2 


2-16 


10-80 


14-27 


28-54 


3-57 


1-7 


6-8 


2-04 


9-63 


12-72 


25-54 


3-36 


1-6 


6-4 


1-92 


8-53 


11-27 


22-54 


315 


1-5 


6- 


1-80 


7-50 


9-91 


19-82 


2-94 


14 


5-6 


1-68 


6-53 


8-63 


17-26 


2-73 


1-3 


5-2 


1-56 


5-63 


7-44 


14-88 


2-52 


12 


4-8 


1-44 


4-80 


6-34 


12-68 


2-31 


11 


4-4 


1-32 


4-03 


5-32 


10-64 


2-10 


1- 


4- 


1-20 


3-33 


4-40 


8-81 


1-89 


•9 


3-6 


1-08 


2-70 


3-57 


714 


1-68 


•8 


3-2 - 


•96 


213 


2-81 


5 62 


1-47 


•7 


2-8 


•84 


1-63 


215 


4-30 


1-26 


•6 


2-4 


•72 


1-20 


1-59 


3-18 


1-05 


•5 


2- 


•60 


•83 


M0 


2-20 



CIRCUMFERENCES OF CIRCLES. 163 



TABLES 



CIRCUMFERENCES OF CIRCLES, 

TO THI 

NEAREST FRACTION OF PRACTICAL MEASUREMENT 

ALSO THE 

AREAS OF CIRCLES 

IN INCHES AND DECIMAL PARTS, LIKEWISE IN 

FEET AND DECIMAL PARTS, AS MAY BE 

REQUIRED. 



Rules that may render (lie following Tables more gen- 
erally useful. 

1. Any of the areas in inches multiplied by «04328, 
or the areas in feet multiplied by 6-2.32, the product is 
the number of imperial gallons at 1 foot in depth. 

2. Any of the areas in feet multiplied by -03704, the 
product equal the number of cubic yards at 1 foot in 
depth. 

3. The area of a circle in inches multiplied by the 
length or thickness in inches, and by -263, the product 
equal the weight in lbs. of cast iron. 

Note. — The French cubic metre, or unit of solid measure, 
equal 35-31716 English cubic feet. Also the litre, or unit for 
measures of capacity, equal C10'28 English cubic inches, or 
about -463 of an nnoerial gallon. 



164 



CIRCUMFERENCES AND 



Dia. in 
inch. 









it 



2 in 

n 
n 
n 

H 

2| 
21 
2J 



Circum. 
in incii. 


Area in 
sq. inch. 


•196 


•0030 


•392 


•0122 


•589 


•0276 


•785 


•0490 


•981 


•0767 


1178 


•1104 


1-374 


•1503 


1-570 


•1963 


1-767 


•2485 


1-963 


•3068 


2-159 


•3712 


2-356 


•4417 


2-552 


•5185 


2-748 


•6013 


2-945 


•6903 


3J 


•7854 


3* 

3J 
4* 

5| 


•9940 

1-227 
1-484 
1-767 
2-074 


5* 


2-405 


55 


2-761 


6| 
6| 


3141 
3-546 


7 


3-976 


73 


4-430 


7| 

8* 
8| 


4-908 
5-412 
5-939 


9 


6-491 




AREAS OF CIRCLES. 



165 




166 



CIRCUMFERENCES AND 



Dia. in 
inch. 



Cir. in 
It. in. 



4 Hi 



Area in 
sq. inch. 



Area in 
sq. ft. 



J -7812 
1-806 J 
1-8311 
1-85(32 
1-8816 
1-9071 
1-9328 
1-9586 



1-9847 
1-9941 
2-0371 
2-0637 
20904 
2-1172 
2-1443 
2-1716 



2-1990 

2-2265 
2-2543 
2-2822 
2-3103 
2-3386 
2-3670 
2-3956 



Dia. in 
inch. 

23 

23£ 

23\ 

23f 

23£ 

S3§ 

23| 

231 



Cir. in Area in Area in 
ft. in. sq. inch. sq. ft. 



615-753 
626-798 
637-941 
649-182 
660-521 
671-958 
683-494 
695-128 



2-8903 
2-9100 
2-9518 

2 9937 
3-0129 
30261 
3-0722 

3 1081 

31418 
3-2075 
3-2731 
3-3410 
3-4081 
3-4775 
3-5468 
3-6101 

3-6870 
3-7583 
3-8302 
3-9042 
3-9761 
4-0500 
4-1241 
4-2000 



4-2760 
4-3521 
4-4302 
4-5083 
4-5861 
4-6665 
4-7467 
4-8274 

4-9081 
4-9901 
50731 
51573 
5-2278 
5-3264 
5-4112 
5-4982 



=5= 









AREAS OF CIRCLES. 167 


— . _ 


Hi a 




Cu 


. in 


Arra in 


Area in 


Di-i 


. in 


Cir. in 


Area in 


Area in 






ft 


in. 


ft. 
8 


m. 

44 


sq. incli. 


sq. ft. 


ft. 


in. 


ft. in. 


sq. in. 
1385-44 


sq. ft- 
9-6212 




9 


R 


801-249 


5-5850 


3 


6 


10 11* 




f 


Ri 


8 


5;, 


816-865 


5-6729 


3 


64 


11 03 


1401-98 


9-7.364 






t) 


4 
f 


8 


GJ 


829-578 


5-7601 


3 


64 


il H 


1418-62 


9-8518 






! 


8 


t>: 


842-390 


5-8491 


3 


6,<j 


11 n 


1435 36 


9-9671 






i 


8 


7J 


855-300 


5-9398 


3 


7 


11 3 


1452-20 


10-084 






) 


94 


8 


i 


868-308 


6-0291 


3 


7j 


11 33 


1469-14 


10-202 






I 


8 


881-415 


6-1201 


3 


% 


11 4l 


1486-17 


10-320 






2 


8 


10 


894-619 


6-2129 


3 


% 


11 6| 


1503-30 


10-439 




2 


10 


3 


1C| 

1 


907-922 


6-3051 


3 


8 


11 5| 


1520-53 


10 559 




2 


lllj 


o 


921-323 


6-3981 


3 


8 | 

8.4 


11 7 


1537-86 


10-679 






2 


H)J 


9 


934 822 


6-4911 


3 


11 1% 


1555-28 


10-800 






2 


lOf 


9 


948-419 


6-5863 


3 


s* 


11 8^ 


1572-81 


10-922 






2 


n 1 


9 


n 

3j 


962115 


6-6815 


3 


9 


11 9? 


1590-43 


11044 






2 


ii} 


•J 


975-908 


6-7772 


3 


n 


11 104 


1008- 15 


11-167 






2 


n,- 1 


9 


98H-800 


6 8738 


3 


94 


11 log 


1625-97 


11-291 






2 


»i 


9 


H 


1003-79 


6-9701 


3 


n 


11 11*. 


1643-89 
166190 


11-415 
11-534 




3 





9 


5 


1017-87 


7-0688 


3 


10 


12 0£ 
12 l£ 




3 


°i 


9 


5Z 


103206 


7-1671 


3 


101 

io2 


1680-02 


11-666 






3 


r2 


9 


6§ 


1046-35 


7-2664 


3 


12 2 


1698-23 


11-793 






3 


(, i 


9 


7J 


1060-73 


7-3662 


3 


103 


12 n 


1716-54 


11-920 






3 


i 


9 


!; i 


1075-21 


7-4661 


3 


11 


12 3$ 


1734-94 


12-048 






3 


»1 


9 


9 


1089-79 


7-5671 


3 


ill 


12 4£ 


1753-45 


12-176 






3 


9 


92 


1104-46 


7-6691 


3 


12 54, 


1772-05 


12-305 






3 


9 


l!, i 


1119-24 


7-7791 
7-8681 


3 
4 





12 6 


1790-76 


12-435 




3 


2 


9 


Hi 


113412 


12 6f 

12 7£ 


1809-56 


12-566 




g 


n 

2f 


10 


oj( 


1149-09 


7-9791 


4 


l\ 


1828-46 


12-697 






3 


10 


01 


116416 


8-0816 


4 


12 8g 
12 9£ 


1817-45 


12-829 






3 


10 


1! 


1179-32 


81891 


4 


0$ 


1866-55 


12-962 






3 


3 1 


10 


1194-59 


3-2951 


4 


1 


12 9£ 


1885-74 


13095 






3 


3J 

3J 

33 


in 


H 


1209-95 


8-4026 


4 


11 


12 105 
12 llj 


190503 


13-229 






3 


K) 


4 


1225-42 


8-5091 


4 


1924-42 


18-364 






3 


10 


4£ 


1240-^8 


8-6171 


4 
4 


2 


13 0^ 


1943-91 


13-499 




3 


4 


10 


5| 


1266-64 


8-7269 


13 1 


1963-50 


13-635 




3 


11 


10 


68 


' 1272-39 


8-8361 


4 


1 


13 11 


1983-18 


13-772 






3 


10 


i\ 


1288-25 


8-9462 


4 


13 2£ 


2002-96 


13-909 






3 


• ! 1 


10 


8 


1304-20 


9 0561 


4 


2* 


13 3| 


2022-84 


14047 






3 


5 


10 


83 


1320-25 


9- 1686 


4 


3 


13 4» 


2042-82 


14186 






3 


54 


10 


Ml 


1336-40 


9-2112 


4 


33 


13 5 


2062-90 


14325 






3 


5j 


10 101 


1362-65 [9-3936 


4 


13 5§ 


2083-07 


1 M65 






3 


5| 


iio ni 


1369-00 IV-5061 


J 4 


33J13 6<| 


2103-35 


14-606 








15 




i 
1 



A (58 



CIRCUMFERENCES AND 



Dia. in 
ft. in 



Cir. in 
ft. in. 



15 6| 

15 6J 

15 61 

15 7| 



15 8£ 
15 94 
15 10 
15 10| 

15 ll| 

16 03 
16 lj 
16 \% 



Area in 
sq. inch. 



2123-72 
2144-19 
2 J 64-75 
2185-42 
2206-18 
2227-05 
2248-01 
2269-06 



2290-22 
2311-48 
2332-83 
2354-28 
2375-83 
2397-48 
2419-22 
244107 

246301 
2485-05 
2507-19 
2529-42 
2551-76 
2574-19 
2596-72 
2619-35 



2642-08 
2664-91 
2687-83 
2710-85 
2733-97 
2757-19 
2780-51 
2803-92 

2827-44 
2851-05 
2874-7(5 
2898-56 
2922-47 
2946-47 
2970-57 
2994-77 



Area injiDia. in 

: u. ft. | ft. in. 



1 1-748 
14-890 
15 033 

15176 
i5-320 
{ 5-465 
15-611 

15-757 



15-904 

16-051 
16-200 
16-349 
16-498 
16-649 
16-800 
16-951 



17101 
17-257 
17-411 
17-565 
17-720 
17-876 
18-033 
18189 



18-347 
18-506 
18-665 
18-825 
18-985 
19147 
19-309 
19-471 



19-635 
19-798 
19-963 
20-128 
20-294 
20-461 
20-629 
20-797 



a 



10 

104 

IQJ 

103 
11 



Cir. in 

ft. in. 

16 24 

16 3J 

16 44 

16 5jf 

16 51 

16 6* 

16 74 

16 84 



17 3| 

17 4* 

17 4* 

17 5£ 

17 6A 

17 7| 

17 8 

17 85 



17 98 
17 101 
17 111 

17 U£ 

18 0§ 
18 lj 
18 21 
18 34 



Area in 
sq. inch, 



3019-07 
3013-47 
3067-96 
3092-56 
3117-25 
314204 
3166-92 
3191-91 

3216-99 
3242-17 
3267-46 
3292-83 
3318-31 
3343-88 
3369-56 
3395-33 

3421-20 
344716 

3473-23 
3499-39 

3525-66 
3552-01 
357S 47 
360503 



Area in 

sq. ft. 



20-965 
21135 
21-305 

21-476 
21-647 
21-819 

21-992 
22-166 



3631-68 
365S-44 
3685-29 
3712-24 
3739-28 
3766-43 
3793-67 
3821-02 



22-333 
22-515 
22-621 
22-866 
23043 
23-221 
23-330 
23-578 

23-758 
23-938 
24-119 
24-301 
24-483 
24-666 
24-350 
25031 



25-220 
25- 105 
25-592 
25-779 
25-964 
26-155 
26-3 W 
26-531 



3848-46 
3875-99 
3903-63 
3H3I-36 27-301 
3959-20 J 27 -494 
3987-13 127-688 



26-725 
26-916 
27108 



114118 
11* 18 

I if! 18 9|| 4013-28 128-078 



4015-16 [27-883 



AREAS OF CIRCLES. 



m 



Dia. in 
il. in. 



6 
6 OJ 




6 11] 



Cir. in 
ft. in. 



Area in 
sq. in. 



20 10£ 



5 4778-37 
5f 4809-05 
6? 4839-83 
J4870-70 
4901-68 
4932-75 
496392 
4995-19 



.n 



20 114 

21 0| 
r21 0* 



5026-26 
505802 
5089-5S 
5121-24 



215153-00 



21 34 51 84-86 



4 |5216-82 
4| 15248-87 



Area in 
sq.ft. 

33183 

33-396 
33-619 
33-824 
31039 
34-255 
34-471 
34-688 



34-906 
35125 
35-344 
35-564 
35-784 
36006 
36-227 
36-450 



21 5£i528 1-02 36-674 

21 6| 5313-27,36-897 

21 7J 5345-62 ! 37-122 

21 7£ 5378-07J37-347 

21 8| 5410-62|37-573 

21 9j 5443-26 37-700 

21 lo| 5476-00 38-027 

21 11 5508-84 38-256 



170 CIRCUMFERENCES AND 






Diam in 1 
ft. and in. 


Circum. in 
ft. and in. 


Area in feot. 


Diam. in 
ft. and in. 


Circum. in 
ft. and in. 


Area in feet. 




7 


21 111 


384846 


10 


31 5 


78-5400 






1 


22 3 


39-4060 


1 


31 81 


79-8540 






2 


22 6} 


40-3388 


2 


31 1IJ 


81-1795 






3 


22 94, 


41-2825 


3 


32 2| 


82 5160 






4 


23 Of 


42-2367 


4 


32 5i 


83-8627 






5 


23 24 


43 2022 


5 


32 8§ 


85-'* 






6 


23 6% 


44-1787 


6 : 


86-" 






7 


23 11 


45-1656 


i 


33 21 


87-96;'? 






8 


24 n 


46-1638 


8 


33 61 


89-3608 






9 


24 4g 


47- 1730 


9 


33 94 


90-7627 






10 


24 7j 


48-1926 


10 


34 Of 


92 1749 






11 


24 108 


49-2236 


11 


34 34 


93-5986 




8 


25 14 


50-2656 


11 


34 6| 


950334 






1 


25 4| 


51-3178 


1 


34 9| 


96 4783 






2 


25 71 


52-3816 


2 


35 01 


97-9347 






3 


25 11 


53-4562 


3 


35 44 


99-4021 






4 


26 21 


54-5412 


4 


35 7{ 


100-8797 






5 


26 5j 


55-6377 


5 


35 10| 


102-3089 






6 


26 8g 


56-7451 


6 


36 H 


103-8691 






7 


26 114 


57-8628 


7 


36 4£ 


105-3794 






8 


27 2| 


58-9920 


8 


36 71 


106-9013 






9 


27 51 


60- 1321 


9 


36 10J 


108-4342 






10 


27 9 


61-2826 


10 


37 21 


109-9772 






11 


28 0i 


62-4445 


11 


37 54, 


111-5319 




9 


28 34, 


63-6174 


12 


37 8§ 


113-0976 






1 


28 6| 


64-8006 


1 


37 114 


114-6732 






2 


28 94 


65-9951 


2 


38 2& 


116-2607 






3 


29 0| 


67-2007 


3 


38 5| 


117-8590 






4 


29 31 


684166 


4 


38 81 


1194674 






5 


29 7 


69-6440 


5 


39 


121 0876 






6 


29 101 


70-8823 


6 


39 31 


122-7187 






7 


30 \\ 


72- 1309 


7 


39 6§ 


124 3598 






8 


30 4| 


73-3910 


8 


39 94 


1260127 






9 


30 ' 7k 


74-6620 


9 


40 0| 


127-6765 






10 


30 111 


75-9433 


10 


40 31 


129-3504 






11 


31 1| 


77-2362 


11 


40 61 


131 3360 

















AKKAS 0* 


CIRCLES. 171 




Diam. in 
ft. ar-d in. 


Circum. in 
ft. and in. 


Area in feet. 


Diam. in 
ft. and in. 


Circum. ir. 
ft. and in. 


Area In feet. 






13 


40 10 


132-7326 


16 


50 3J 


2010624 






1 


41 li 


134-4391 


1 


50 64 


2031615 






2 


41 4| 


1361574 


2 


50 9| 


205-2726 






3 


41 7? 


137-886? 


3 


51 0£ 


207-3946 






4 


41 10§ 


139-6260 


4 


51 3| 


209-5264 






5 


42 1| 


1413771 


5 


51 6h 


211-6703 






6 


42 4i 


143-1391 


6 


51 10 


213-8251 






7 


42 8 


144D111 


7 


52 1* 


215-9896 






8 


42 111 


1460949 


8 


52 44 


2181662 






9 


43 2i 


148-4896 


9 


52 7§ 


220-3537 






10 


43 5.5 


150-2943 


10 


52 10£ 


222-5510 






11 


43 8g 


152 1109 


11 


53 1| 


224 7603 




14 


43 Ui 


153-9384 


17 


53 4} 


226-9806 




1 


44 % 


155-7758 


1 


53 8 


229-2105 






2 


44 6 


157-6250 


2 


53 Hi 


231-4625 






3 


44 9x 


159-4852 


3 


54 2J 


233-7055 






4 


45 04 


161-3553 


4 


54 5| 


235-9682 






5 


45 3£ 


163-2373 


5 


54 8£ 


238-2430 






6 


45 6| 


1651303 


6 


54 11| 


240-5287 






7 


45 9| 


167-0331 


7 


55 2§ 


242-8241 






8 


46 05 


168-9479 


8 


55 6 


2451316 






9 


46 4 


170-8735 


9 


55 9J 


247-4500 






10 


46 7J 


172-8091 


10 


56 04 


249-7781 






11 


46 1U 


174-7565 


11 


56 34 


252 1184 




15 


47 U 


176-7150 


18 


56 6h 


254-4696 




1 


47 4| 


176 6832 


1 


56 91 


256-8303 






2 


47 71 


180-6634 


2 


57 05 


259-2033 






3 


47 log 


182-6545 


3 


57 4 


261-5872 






4 


48 2h 


184-6555 


4 


57 7l 


263-9807 






5 


48 5J 


186-6684 


5 


57 10 1 


266-3864 






6 


48 8k 


1886923 


6 


58 1| 


268-8031 






7 


48 11| 


190-7260 


7 


58 4£ 


271-2293 






8 


49 2& 


192 7716 


8 


58 7| 


273-6678 






9 


49 5 3 4 


194-8232 


9 


58 10-] 


2761171 






10 


49 81 


1968946 


10 


59 2 1278-5761 






11 


50 


198-9730 


11 


59 5| | 281-0472 








15* 











» 




172 SQUARE AND CUBE R001S OF NUMBERS- 






No. 


S. R. 


C. R. 


Mo. 


S. R. 


C. R. JNu. 


S. R. 
10-4403 


C. R. 


No. | S. K. ; C. R. 




1 


1-0O0C 


l-oooo 


15 


7-4151 


3-8029 1 109 


4-7763 


163! 12-7671 5-4625 






2 


1-4142 


1-2599 


56 


7-4833 


3-8258 


110 


10-1880 


4-7914 


164 12-3052 ! 5-4737 








a 


1-7320 


1-44232 


57 


7-5498 


3-3485 


111 


10-5356 


l-Sii.58 


165 


12-3452 5-4818 








4 


2-0000 


1-5374 


53 


7-6157 


3 8703 


112 


10-5330 


4-8202 


166 


12-8319 


5-4958 








5 


2-2360 


1-7099 


59 


7-6311 


3 8929 


113 


10-6801 


4-8345 


,6, 


12-9-28 


5-5068 








6 


2-4494 


1-3171 


fio 


7-7459 


3-9148 


111 


10-6770 


4-3488 


163 


12-9014 


5-5178 








7 


2-64.57 


1-9129 


61 


7-8102 


3-9364 


115 


10-7238 


4-85 29 


169 


13-0000 


5-5 287 








8 


2 8284 


2-0000 


82 


7-8740 


3-9-578 


116 


10-7703 


4-8769 


170 


13-0384 


5-5396 








9 


3 0000 


2-0800 


63 


7-9372 


3-97-0 


117 


10-3166 


4-3909 


171 


13-0766 


5-5404 








10 


3-1622 


2-1544 


64 


8-0000 


4-0000 


11 1 


10-8627 


4-9048 


172 


13-1118 


5-561-2 








11 


3-3 165 


2-2239 


65 


8-0522 


4-0207 Ill9 


10-9087 


4-91*5 


173 


13-15:9 


5-5720 








12 


3-4641 


2-2894 


66 


8-1-240 


4-0412 120 


'.O-i.514 


4-93*4 


1 J ; 


13-1909 


5-58 ,-7 








13 


3 6055 


2-8513 


67 


8-1853 


4-0615 121 


11-0000 


4-9450 


17 7 


13-2 237 


5-5934 








14 


3-74 16 


2-4101 


68 


8-2462 


4-0816' 122 


11-04 53 


4-95jii 


176 


13-2634 


5-6040 








Id 


3-87^9 


2-4662 


69 


8-3056 


4 1015(123 


11-0903 


4-9731 


177 


13-3041 


5-S4IB 








16 


4-U000 


2-5198 


70 


8-3655 


4-1212; 124 


11 1355 


4-L-356 


173! 13-3416 


5-6252 








17 


4-1231 


2-5712 


71 


8-4261 


4-1408 




111303 


5 f'000 


1791 13-3790 


5-6357 








18 


4-2426 


2-5207 


72 


8 4852 


4-1601 


1-26 


11-2.49 


5-0132 


180 1 13-4164 


5-6462 








19 


4-3588 


2-6681 


73 


8-5140 


4-1793 


127 


ll--6l;4 


j-U-AJ 


1-1 13-4586 


5-8598 








% 


4-4721 


2-7144 


71 


8-60-23 


4-1933 




11-3137 


5-0396 


182 l3-49'i7 


5-5670 








21 


4-5325 


2-7589 


7 5 


8-6602 


4 2171 


129 


11 -.'573 


5-0,27 


|-3| 13-5277 


.5-6774 








22 


4-6904 


2' -020 


76 


8-7177 


4 ■2353 


130 


11-4017 


5-0 57 


184 13-5646 


5-6877 








23 


4-7958 


2-8438 


77 


8 7749 


4-2543 


131 


11 -4 455 


5-0737 


1«5 


13-6014 


5- 6 980 








24 


4-8989 


2- 8s 4 4 


78 


8-83:7 


4-2726 


132 


11-4891 


5-0916 


136 


13-6331 


5-7082 








23 


50000 


2-9240 


79 


8-8881 


4-2903 


133 


11-53-5 


5-1044 


187 


13-5747 


5-7184 








■26 


5-0990 


2-9624 


80 


8-9-14 2 


4-3038 


131 


1 1 -5753 


5- 1172 


188 


13-7113 


5-7236 








27 


5-1961 


3-0. '00 


Bl 


9-0000 


4-3287 


135 


11-6189 


5-1299 


189 


13-7477 


5-7337 








28 


5-2915 


3-0.65 


82 


9-0553 


4-3444 


136 


11-6519 


5-1425 


190 


13-7840 


5-7488 








29 


5 3S51 


3-0723 


S3 


9-1104 


4-3320 


137 


11-7045 


5- 1551 


191 


13 8202 


5-7539 








30 


5-1772 


3-1072 


84 


9-1651 


4-3795 


138 


11-7473 


5-1676 


1 92 


13-8564 


5-7689 








31 


5 5677 


3-1413 


85 


9-2195 


4 3968 


139 


11-7398 


5-1801 


1 93 


13-89-4 


5-7739 








32 


5 6568 


3-1743 


S3 


9-2736 


1-4M0 


140 


11-8321 


5-1924 


194 


13-9283 


5-7889 








33 


5-7445 


3-2075 


87 


9-3273 


4-4310 


141 


11-8743 


5-2018 


195 


13-S642 


5-7938 








34 


5-8309 


3 2395 


89 


9 3308 


4-4479 


11: 


11-9163 


5-2171 


195 


14-0000 


5-8087 








35 


5-9160 


3-2710 


.-.9 


9'4339 


4-4647 


143 


11-9582 


5-2293 


197 


140356 


5-8185 








36 


6-0000 


3-3019 


9l> 


9-4868 


4-4814 


144 


12-0000 


5-2414 


153 


140712 


5-8284 








37 


6-0327 


3-332-2 


91 


9-5393 


4-4979 


145 


12-0415 


5-2535 


15=9 


14-1067 


5-8582 








33 


6 1644 


3-3619 


9J 


9-5916 


4-5143 


U6 


12-0830 


5-2656 


200 


14-1421 


5-8430 








39 


6-2449 


3-3912 


93 


9-6436 


4-5306 


147 


121243 


5-2776 


201 


14-1774 


5-8577 








40 


6-3245 


3-4199 


91 


9-6953 


4-5458 


MS 


12-1655 


5-2895 


202 


14-2126 


5-8674 








41 


6-4031 


3-4482 


95 


9-7-167 


4-5629 


179 


12-2055 


5-3014 


•203 


14-2478 


5-8771 








42 


6-4S07 


3-4760 


96 


9-7979 


4-5788 


159 


12-2474 


5-3132 


204 


14-2828 


5-3867 








43 


6-5574 


3-5033 


97 


S-8483 


4-5947 


151 


12-2832 


5-3250 


205 


14-3178 


5-89*3 








4-1 


6-633' 


3 5303 


93 


9-«994 


4-6104 


152 


12-3238 


5-?35ir 


205 


14-3527 


5-9059 








45 


6-7082 


3-55:8 


99 


9-9(98 


4-6260 


153 


12-3693 


5-3484 


207 


14-3874 


5-9154 








46 


6-7823 


3-5830 


llill 


10-0000 


4-6415 


15-1 


12-4095 


5-3601 


208 


14-4222 


5-9249 








47 


6-3556 


3-60s8 


»01 


10-0498 


4-6570 


1 55 


12-4498 


5-3716 


209 


14-4568 


5-9344 








43 


6-9282 


3-6342 


102 


10-0995 


4-6723 


156 


12-4899 


5-3832 


210 


14-4913 


5-9439 








49 


7-0000 


3-6593 


1(13 


10-1488 


4-6875 


1.57 


12-5299 


5-3946 


211 


14-5258 


5-95.33 








50 


70710 


3-6340 


104 


10-1980 


4-7026 


158 


12-5f,93 


5-4061 


212 


14-5602 


5-9627 








51 


71414 


3-7084 


105 


10-2469 


4-7176 


159 1 12-6095 


5-4175 


213 


14-5945 


5-9720 








5'2 


7-2111 


3-73-2.5 


106 


10-2956 


4 -7326 [160 12-6491 5-4288 


214 14-6287 15 9814 








53 


7-2801 


3-7562 


107 


10-3440 


4-7474| 161 i 12-6385 5-4401 


215. 14-6628; 5 9907 








54 


7-3434 


3-7797 


108 


10-3923 


4-7622} 162 12-7279 5-4513 215 i 14-6969 6 0000 






7'ojlnd the square or cube root of a number consisting of integers and decimals. 






Rale. — Multiply the difference ketween the root of the integer part of the git-ei 




sumber, and the root of the next higher number, by the decimal part of the ^t?m 
Dumber, and add the product to the root of the given integer number; the sum is the 






»»t required. 




Ex. Required the square root of 20-321. 




Square root of 21 «= 4-5825 




M •« «« 20=4-472! 




Diff. — -1104 X -321 + 4-4721 —4-507. Ac, the root reqoired. 

■• ■ - 



VARNISHES. 173 



MISCELLANEOUS NOTES 

VARNISHES. 

[From Dr. Ure's Dictionary of Arts and Manufactures J 

White Spirit Varnish. — Sandarach, 250 parts ; mas 
tic in tears, 64 ; elemi resin, 32 ; Venice turpentine 
64; alcohol of 85 per cent, 1000 parts by measure 
The turpentine is to be added after the resins are dis- 
solved. This is a brilliant varnish, but not so hard as 
to bear polishing-. 

Varnish for the Wood Toys of Spa. — Tender copal, 
75 parts ; mastic, 12-5 ; Venice turpentine, 6*5 ; alcohol 
of 95 per cent, 100 parts by measure ; water, ounces — 
for example, if the other be taken in ounces. The 
alcohol must be first made to act upon the copal, with 
the aid of a little oil of lavender or camphor, if thought 
fit ; and, the solution being passed through a liner, 
cloth, the mastic must be introduced. After it is 
dissolved, the Venice turpentine, previously melted in 
a water bafh, should be added. The lower the tem- 
perature at which these operations are carried on, the 
more beautiful will the varnish be. This varnish ought 
to be very white, very drying, and capable of being 
smoothed with pumice-stone and polished. 

Varnish for Cabinet-Makers. — Pale shellac, 750 
parts ; mastic, 64 ; alcohol of 90 per cent, 1000 parts 
by measure. The solution is made in the cold, with 
the aid of frequent stirring. It is always muddy, and 
\s employed without being filtered. With the saone 
resins and proof spirit, a varnish is made for the book- 
binders, to do over their morocco leather. 

Crystal Varnish. — Procure a bottle of Canada bal- 
sam, which can be had at any druggist's ; draw out the 
cork and set the bottle of balsam at a little distance 



. 74 MISCELLANEOUS NOTES. 

from the fire, turning it round several times, until the 
heat has thinned it ; then have something that wil} 
hold as much as double the quantity of balsam ; carry 
the balsam from the fire, and, while fluid, mix it with 
the same quantity of good turpentine, and shake them 
together until they are well incorporated. In a few 
days, the varnish is fit for use; particularly if it is 
poured into a half-gallon glass or stone bottle, and kept 
in a gentle warmth. This varnish is used for maps* 
prints, charts, drawings, paper ornaments, &c. 

The Chinese Varnish is obtained from a tree which 
grows in Cochin-China, China, and Siam. It forms 
the best of all varnishes. 

Gold Lacker. — Put into a clean four-gallon tin 1 lb. 
ground turmeric, ij oz. powdered gamboge, 3£ lbs. 
powdered gum sandarach, % lb. snellac, and 2 galls, 
spirits of wine. After being dissolved and strained, 
add 1 pint of turpentine varnish, well mixed. 

Red Spirit Lacker. — 2 galls, spirits of wine; 1 lb. 
dragon's-blood; 3 lbs. Spanish annotto; 3£ lbs. gum 
sandarach ; 2 pints turpentine ; — made exactly as the 
gold lacker. 

The Varnish of JVatin, for Gilded Articles. — Gum 
lac in grain, 125 parts ; gamboge, 125 ; dragon's-blood, 
125; annotto, 125; saffron, 32. Each resin must be 
dissolved in 1000 parts by measure of alcohol of 90 
per cent. Two separate tinctures must be made with 
the dragon's-blood and annotto, in 1000 parts of such 
alcohol; and a proper proportion of each should be 
added to the varnish, according to the shade of golden 
color wanted. 

Transfer Varnish. — For fixing engravings or litho- 
graphs upon wood, a varnish called mordant is used in 
J^rance, which differs from others chiefly in containing 
more Venice turpentine, to make it sticky. L consists 
of sandarach, 250 parts ; mastic in tears, 64 ; rosin^ 
125; Venice turpentine, 250; alcohol, 1000 parts by 
peasure. 

Common Mastic Varnish. — Put as much gum mastic. 



VARNISHES. 175 

unpicked, into the gum-pot, as may be required ; and 
to every 2% lbs. of gum, pour in 1 gall, of cold turpen- 
tine ; set the pot over a very moderate fire, and stir it 
Be careful, when the steam of the turpentine rises near 
the mouth of the pot, to cover with a piece of woollen 
cloth, and carry it out of doors, as the vapor is very ap' 
to catch fire. A few minutes' low heat will perfectly 
dissolve 8 lbs. of gum, which will, with 4 galls, of 
turpentine, produce, when strained, 4.^ galls, of varnish; 
to which add, while yet hot, 5 pints of pale turpentine 
varnish, which improves the body and hardness of the 
mastic varnish. 

Pale Brass Lacker. — 2 galls, spirits of wine; 3 oz. 
Cape aloes ; cut small 1 lb. fine pale shellac ; 1 oz. 
gamboge, cut small; no turpentine; — varnish made 
exactly as before. But observe, that those who make 
lackers frequently want some paler and some darker ; 
and sometimes inclining more to the particular tint of 
certain of the component ingredients. Therefore, if a 
4 oz. phial of a strong solution of each ingredient be 
prepared, a lacker of any tint can be produced at any 
time. 

Iron-Work Black. — Put 48 lbs. asphaltum into an 
iron pot, and boil for 4 hours ; during the first 2 hours, 
introduce 7 lbs. litharge, 3 lbs. dried copperas, and 10 
galls, boiled ; add 1-eighth lb. run of dark gum, with 
2 galls, hot oil. After pouring the oil and gum, con- 
tinue the boiling 2 hours, or until it will roll into hard 
pills, like Japan. When cool, thin it off with 30 galls, 
turpentine, or until it is of proper consistence. This 
varnish is intended for the iron-work of coaches and 
other carriages, &c. 

To make Cloth, Silk, fyc. umlcr-proof. — Mix equal 
quantities of alum and acetate of lead, and dissolve 
the mixture in a gallon and a half of boiling water 
When the solution has cooled, remove the supernatant 
liquid from the sediment, which consists of sulphate of 
lead, and it is ready for use. Any article of dress, 
wnen well saturated in this liquid, and allowed to dry 



176 SOLDERS. 

Blowly, bears the action of boiling water, and does not 
permit it to pass through, although steam and air pene- 
trate it freely. 

Cement for China, Glass, tfc. — To 1 oz. gum mastic 
add as much spirits of wine as will dissolve it ; soak 
1 oz. isinglass in water till it is quite soil, then dis- 
solve it in pure brandy till of the consistence of glue ; 
to this add \ oz. gum ammoniac, well rubbed and 
mixed. Put now the two mixtures together in a vessel 
over a gentle heat, till properly united, and the cemen' 
is ready for use. It must be kept in a phial wel 
stopped ; and, when about to be used, it ought to bi 
set in boiling water to soften. 

Preparation for Silver Solution. — Take 1 pint of 
pure rain or distilled water; add to it 2 oz. cyanide of 
potassium ; shake them together occasionally, until the 
latter is entirely dissolved, and allow the liquid to 

come clear ; then add | oz. oxide of silver, which 
will very speedily dissolve ; and, after a short time, s 
clear, transparent solution will be obtained. 

Preparation of Gold Solution. — Warm a pint of 
pure rain water, and dissolve in it 2 oz. cyanide of 
potassium ; then add | oz. oxide of gold ; the solution 
will at first be yellowish, but will soon subside to white 



SOLDERS. 

For Lead. — Melt 1 part of block tin, and, when in 
a state of fusion, add 2 parts of lead. Resin should be 
used with this solder. 

For Tin. — Pewter, 4 parts ; tin, 1 ; bismuth, 1 ; melt 
them together. Resin is also used with this solder. 

For Iron. — Tough brass, with a small quantity of 
borax. 



SCREWS. 



177 



CAPACITY OF CISTERNS IN GALLONS. 



For each 10 Inches in Depth. 



2 feet diameter, . 


19-5 


8 feet diameter, 


313-33 


U " " 


30-6 


8£ " 


. * 353-72 


3 « 


44-06 


9 « 


. 396-56 


3i " " 


59-97 


H " " 


. 461-40 


4 " 


. 78-33 


10 " « 


. 489-2C 


4£ « 


99-14 


n « " 


. 592-4C 


r « « 


12240 


12 « 


. 705- 


5A « 


145-10 


13 « « 


. 8274 


6 5 « 


176-25 


14 « 


. 959-6 


6i « 


206-85 


15 " « 


. 11016 


7 3 « 


. 239-88 


20 « " 


. 19584 


7A « « 


27540 
SCR] 


25 " « 
SWS. 


. . 3059-9 



Table showing the Number of Threads to an Inch in 
V -thread Screivs. 



Diim. in inches, . 
No. of threads, . 


.20 


18 


1 A * * f J i i* i* 

16 14 12 11 10 9 8 7 7 


If 
6 


Diam. in inches, . 
No. of threads, . 


. 6 


It 
5 


1| 1$ 2 2| 2^ 2| 3 3| 
5 4 4^ 4 4 3A. 34 3.} 


3A 
3:1 


Diam. in inches, 
No. of threads, . 


.31 
. 3 


4 
3 


4J 44 4| 5 5| 54 5f 

2£ 2| 2| 2| 2f 2$ 2£ 


6 



The depth of the threads should be half their pitch. 
The diameter of a screw, to work in the teeth of a 
wheel, should be such, that the angle of the threads 
does not exceed 10°. 





178 WEIGHTS OF VARIOUS SUBSTANCES. 

RECAPITULATION OF WEIGHTS OF VARIOUS 
SUBSTANCES. 


Names. 


Cubic foot in lbs. 


Cubic inch in lbs 

•2607 

•2816 

•2834 

•321 18 

•41015 

•3112 

•263 

•0171 

•03721 

•03616 


Cast iron 
Wrought iron 
Steel . . . 
Copper . . 
Lead . . . 






450-55 

486-65 

489-8 

555- 

708-75 

537-75 

456- 

29-56 

64-3 

62-5 
•07529 
•03689 


Brass . . . 




Tin .... 




White pine . 
Salt water (sea' 
Fresh water 
Air .... 




Steam . . . 




Cast Iron expands -j ^Wtf of its length for one 
degree of heat; greatest change in the shade, in this 
climate, ttV?i or * * ts length » exposed to the sun's rays* 
Y*r\ny ; shrinks in cooling from ^ to -^ °f i ts length : 
is crushed by a force of 93,000 lbs. upon a square inch ; 
will bear, without permanent alteration, 15,300 lbs. upon 
a square inch, and an extension of tsW oi * i ts length. 
Weight of modulus of elasticity for a base of an inch 
square, 18,400,000 lbs.; height of modulus of elasticity, 
5,750,000 feet. 

Wrought Iron expands T ^ n'^^ of its length for 

out permanent alteration, 17,800 lbs., nnd an extension 
Dy an increase of one degree of heat. Weight of 

2-1,920,000 lbs. ; height of modulus of elasticity 
7,550,000 feet 



PART SECOND. 



INTRODUCTION. 



CHOICE OF A PROFESSION: RESPECT AIM 
LITY OF MECHANICAL TRADES. 

The choice of a pursuit in life, one of the 
most important practical questions upon which 
a young person is ever called to decide, is often 
determined by the most trifling circumstances, 
and without the slightest aid from judgment or 
reflection. One youth becomes a soldier be- 
cause his great grandfather was at the taking 
of Cape Breton, or his great uncle signalized 
himself in Braddock's fight; another studies 
medicine, and hopes to be almost an infallible 
doctor, because he is the seventh son of a 
seventh son ; while a third chooses the profes- 
sion of the law for no better reason than that 
his sponsors at the baptismal font, chose to 
call him William Wirt, or Daniel Webster, or 
John Sergeant. Surely this is not that practi- 
cal wisdom which adapts the fittest means to 
the noblest ends The choice o r a profession 
IB 



|§0 INTRODUCTION 

in life is at least worthy of such a considera- 
tion as common sense would dictate in any 
other case, where success in an enterprise de- 
pends upon fitness for undertaking it. Men do 
not expect to gather grapes from thorns, nor 
figs from thistles; yet they expect their sons 
and daughters to succeed in pursuits for which 
they are wholly incapacitated by talents, dispo- 
sition or education ; and what is still more un- 
reasonable, they expect them to be happy in 
situations which are totally uncongenial to their 
nature. 

One reason why parents and guardians fall 
so frequently into errors on this point, — errors, 
too, which they lead those under their charge 
to embrace, — is the vain imagination that there is 
a great and essential difference in the respecta 
bility of those pursuits which are generally 
admitted to be honest. The respectability of a 
profession, I suppose it will be admitted, must 
depend in a great measure on the respectable 
character of its members, taken collectively, or 
regarded with reference to the most brilliant 
examples. If we adopt this standard, it will be 
found no easy matter to establish a claim to 
superior respectability in favour of any one 



COMPARISON OF PROFESSIONS 



181 



trade or profession, or of any class of trades 
or professions. 

If it should be asserted that the learned pro- 
fessions of law, physic and divinity are more 
respectable than the pursuits of commerce, me- 
chanics or agriculture, it might be easily shown 
that taken collectively, the members of these 
latter professions or trades possess more wealth, 
ease and independence than those of the learn- 
ed ones ; and moreover, that among them as 
brilliant examples of mental pre-eminence, pa- 
triotism and public spirit may be pointed out 
as among those of the more learned professions 

In fact, in a country like ours, such a claim 
of superior respectability on behalf of any pro- 
fession is preposterous ; and yet it is constantly 
assigned by purse-proud fathers and silly 
mothers as a reason for determining their chil- 
dren's pursuits in life. There is a very general 
impression that a merchant, a clergyman, doc- 
tor or lawyer stands higher, and should stand 
higher, in the social scale than a mechanic or 
tanner. Unt such is not the fact, as a general 
principle; or, which results in the same thing, 
it in a particular instance, a particular merchant, 
for example, stands higher in social estimation 
man a particular mechanic, it is not on accoun* 



JQ2 INTRODUCTION. 

of the respective means by which they earn 
theii livelihood, but because the merchant in 
this instance has claims by wealth, family in- 
fluence or education, which the mechanic has 
not; and by passing into the next street, and 
taking another example, you will find the tables 
completely turned, and the mechanic in the 
enjoyment of a social position to which the 
merchant cannot aspire. This fact is sufficient 
to prove that a ma.n of one trade or profession 
does not take a lower position in society than 
another of a different profession, simply on 
account of the different modes by which they 
subsist, but by reason of other circumstances 
which are wholly independent of this conside- 
ration. Mr. A., who is a merchant, does not, 
for example, decline an intimate acquaintance 
and social intercourse with Mr. B., because Mr. 
B. is a mechanic, but because their favourite 
topics of conversation, their tastes and pursuits, 
are different ; and this is clearly apparent from 
another fact, viz. : — that whenever two persons 
of totally different professions happen to meet 
frequently upon some common ground of 
science or the fine arts, in their leisure hours 
they immediately recognise each other's natu- 
ral equality and become familiar companions 



RESPECTABILITY OF TRADES. 



IS? 



They collect plants, or minerals, or perform 
chemical or philosophical experiments together; 
they unite in the same pursuits during their 
leisure hours, and become daily moie and more 
assimilated in mind and character, as well as 
in their favourite recreations, until they are 
bound together by the strictest bonds of friend- 
ship. There is, therefore, no necessary or e« 
sential difference in the respectability of differ- 
ent trades and professions ; and there is no 
social estrangement between their members, 
which may not be overcome by precisely the 
same means which constitute the cause of inti- 
macy in other circumstances. In our country, 
therefore, in point of real and essential respect- 
ability, all trades and professions are equal ; and 
the social position which a man enjoys, and 
the degree of respect which he is able to com- 
mand, depend not upon his trade, but upon 
his individual character. 

If, in every part of the United States, the 
stupid prejudice which would exclude the me- 
chanic or the farmer from any society to which 
his intelligence and good manners entitle him, 
is not thoroughly exploded, the time has cer- 
tainly arrived when it is no longer to be avowed 
ov well bred people. In fact, the rule which 
16* 



1S4 



INTRODUCTION. 



would exclude a man from any drawing-room 
in the land, on the simple ground of his bein^ 
a mechanic, would have excluded from the 
same drawing-room such men as Nathaniel 
Bowditch, who was a mariner by trade ; Roger 
Sherman, who was a shoemaker by trade ; Ben- 
jamin Franklin, late ambassador to the Court 
of Versailles, who was a printer by trade ; and 
George Washington, a very respectable man oi 
the last century, who was a surveyor by trade 
But the imaginary respectability which a man 
may happen to enjoy from his position in so- 
ciety, is not by any means the first and most 
im^rtant thing to be considered in the choice 
of a profession. It should not be the leading 
motive in determining the choice of the parent ; 
neither should it be the main consideration in 
the mind of the young person himself. There 
is another, and a much more important poir. 4 - 
which claims and should receive the prece- 
dence. Every parent in making choice of a 
profession for his son, and every son in making 
the same choice for himself, should seriously 
and deliberately inquire, what profession affords 
the best chance for happiness ; — happiness, in 
the noblest and broadest sense — happiness 
which consists in contentment, independence 



RESPECTABILITY OF TRADES. Iga 

Biul real usefulness — happiness, which begins 
in the conscientious and successful discharge 
of duty on earth, and reaches forward to the 
unerring retribution of a future world. 

The inquiry which is thus presented is a 
very extensive one. It admits of whole years 
of investigation — whole volumes of disquisi- 
tion to treat it at large, and apply it to any 
considerable portion of the cases that might 
arise. In order, therefore, to avoid running 
into useless generalities, I shall devote the short 
space which is allotted to me on the present 
occasion, to a very small part of this great sub- 
ject, and shall consider that part in a single 
point of view. I propose, in the outset of the 
present work, to inquire what opportunities are 
afforded for usefulness, happiness, and real re- 
spectability by the mechanical trades — in other 
words, to inquire how a mechanic may be use- 
ful, happy and respectable. In the succeeding 
chapter I shall consider the first branch of tha 
subject 



186 



THE YOUNG MF.P.HANIC 



CHAPTER I. 



l'HE MECHANIC SHOULD BE MASTEK OF 
HIS TRADE. 

In order to become useful, respectable, and 
nappy, it appears to me to be necessary, in the 
first place, that the mechanic should be- 
come a thorough master of his trade. Having 
made a deliberate choice of that pursuit, by 
which he is to gain his livelihood, it is a mat- 
ter of the utmost importance that he should 
devote the energies of his mind to the business 
unreservedly, until he has mastered all its prin- 
ciples and details. It is by this means only 
that he can use it with ease and satisfaction as 
the instrument of success in the world. .The 
incapable, or half taught mechanic, always 
works at a ruinous disadvantage. He can 
neither command the highest prices for the pro- 
ducts of his art, nor superintend with intelli- 
gence and authority the workmen under his 
care. He is in constant danger of failure in his 
business, or of abandoning it, through sheer 
disgust, only to take up some other pursuit for 
which he is totally unfitted by education. I< 



APPRENTICESHIP. JS"? 

is a laudable ambition, therefore, which makes 
him aspire to be first among his fellows. Aid 
Casar aut null us — a master mechanic, or no 
mechanic at all — should be his motto. 

1. In order to render himself a thorough 
proficient in his trade, the mechanic should 
serve out his complete apprenticeship. Justice 
to himself, as well as to his master, dictates this 
course. Nor is it less a matter of policy than 
of moral duty. Even if he should deem him- 
self capable of undertaking the management of 
business for himself before he has half com- 
pleted his apprenticeship, it is a much safer and 
wiser course to remain in a subordinate capa- 
city till he has attained the age of manhood, 
than to rush upon the heavy duties anJ iearful 
responsibilities of active life before his judg- 
ment is matured, his understanding ripened, 
and his nerves hardened for the rough encoun- 
ter of conflicting interests and unforeseen emer- 
gencies. 

2. At the same time that I counsel the ap- 
p-entice to serve out his whole time, 1 would 
strenuously urge upon him the importance of 
devoting any leisure moments that he may have 
at his command, each day, to the cultivation of 
his mind. The parent or guardian, in becoming 



jgg THE \OUNG MECHANIC. 

a party to indentures, should be careful to have 
a clause inserted by which a certain portion of 
time shall be sec. red to the apprentice for men- 
tal cultivation , and when this is done the ap- 
prentice should regularly conseci ite this time 
to its legitimate purpose.*- In our large cities 
facilities for this purpose are judiciously afford- 
ed by the beneficent provisions of Mechanics' 
Institutes, Lyceums and Libraries ; but even in 
situations where such opportunities are not af- 
forded, we know by many illustrious examples 
that knowledge may be pursued and attained 
under the most discouraging difficulties. Where 
that good seed, the love of science, has been 
once implanted, it will spring up and grow and 
flourish, though pelted by storms of adversity, 
and chilled by the coldness of neglect. It is 
this consideration which encourages the teacher 
who has the future apprentice under his care, 
to instil into his opening mind the most liberal 
and exalted views of the real beauty, as well as 
utility, of science and literature. 

But why, it may be inquired, should the me- 
chanic be inspired with the love of science and 
literature? I answer, that the mechanic should 
learn to love these intellectual pursuits for two 



MENTAL CULTIVATION. \Q$ 

reasons: — First, because he is a mechanic; and 
secondly, because he is a man. 

If the physician, the lawyer, the statesman, 
and the divine avail themselves of the assist- 
ance of science and literature in their several 
professions, the mechanic has still stronger in- 
ducements for doing the same thing; for to 
none of these professions are the results of 
science so directly applicable, and for none of 
them are the recreations of literature so appro- 
priate or gratifying. By making himself mas- 
ter of those principles of science which are 
most intimately connected with his trade, the 
mechanic, while he is satisfying a libera! cu- 
riosity, may possibly be approaching some 
brilliant discovery, which will speedily conducf 
him to fortune and fame; and if the lighter 
reading, generally termed literature, promises 
no such result, it affords him the most dignified 
and innocent means of amusement, and pre- 
serves the vigour and increases the brightness 
of his intellect. He should, therefore, learn to 
appreciate such pursuits, because they are fitting 
and proper to him as a mechanic. 

Pie may also claim them as his own, upon 
the broad principle, that wherever there is a 
human intellect to be cultivated, there is a na- 



190 



THE YOUNG MECHANIC 



tural and indefeasible right to the brightest de* 
grree of cultivation which it can attain. 

I remark, in the next place, that the mechanic, 
in order to render himself a complete mastel 
of his trade, should possess himself of new 
discoveries in science which are applicable to 
his purposes, and should actually apply them 
to the improvement of his trade. 

There never was a time since Lord Bacon 
first placed in the hands of philosophy the 
right instrument of investigation, when men of 
science were more actively and successfully 
engaged in developing the materials and pro- 
cesses directly applicable to the advancement 
of the mechanic arts, than the present. The 
forest and the mountain, the mine and the river, 
the deep bosom of the ocean itself — all are 
literally ransacked by the ardent devotees of 
science, in pursuit of new substances which 
may minister to the sustenance or pleasure of 
man, or may open to the gaze of liberal cu- 
riosity the wonders of creative power. The 
pcientinc traveller brings home the products of 
distant lands to be naturalized in his own coun- 
try, and thus supply new materials for the use- 
ful arts; the mechanical philosopher is con- 
stantly adding to the number of known motive 



USE OF LEISURE TIME. JO, 

powers ; the chemist is discovering new sub- 
stances, and making new developements and 
combinations of the powers of those already 
known; while the press, by means of the ait 
preservative of all arts, is bringing the result 
of all these labours and inquiries u home to the 
bosoms and business of men." 

At such a time it becomes not the mechanic 
to be an idle or regardless spectator of all this 
activity. In the leisure moments which, by an 
ordinary arrangement of his labours, every man 
may redeem, he should direct his attention to 
the progress of discovery in chemistry, me- 
chanical philosophy and natural history, which 
have a direct bearing on his trade. He should 
attach himself to that mechanics' institute or 
lyceum which affords him the best means of 
improvement by its lectures, experiments, and 
library. He should cultivate the acquaintance 
of those scientific men who have the good 
sense to appreciate the society of intelligent 
practical mechanics, and he should apply the 
results of his inquiries, so far as it may be ju- 
diciously done, to the perfecting of his own 
manufactures. In recommending such a course 
Jo the young mechanic, I know that I am not 
urging upon him vain speculations in visionary 
17 



192 THE YOUNG MECHANIC. 

schema. That such a course is precisely the 
one best calculated to improve and develope 
the mechanical arts, is clearly apparent when- 
ever an exhibition of the products of American 
industry is opened by any one of the societies 
constituted and supported by mechanics for 
this very purpose. A single exhibition of the 
Franklin Institute establishes with more cer- 
tainty than a whole volume of arguments, the 
soundness of that policy which leads the me- 
chanic to devote his winter evenings to scientific 
pursuits, and to apply the result of bis study 
to the improvement of his own trade. 



ADHERENCE TO TRADE. \Q$ 



CHAPTER II. 

THE MECHANIC SHOULD REMAIN AT 
TACHED TO HIS TRADE. 

This is not all that is requisite for the use- 
fulness, happiness, and respectability of the 
mechanic. In order to secure these objects fully, 
I maintain, in the second place, that it is neces- 
sary for him to remain attached to his trade. 
Recent events in this country have, I think, 
sufficiently demonstrated the pernicious ten- 
dency of that ambitious restlessness which has 
lately pervaded all classes of people, and made 
almost every man regard his business whatever 
it happened to be, as merely the stepping stone 
to something apparently higher. Apparently, 
I say, for we have seen in many instances that 
mechanics, who were slowly and surely ac- 
quiring the means of independence and com- 
fort, have dashed into wild speculations, in 
hopes to rise to some imaginary height of 
wealth and importance ; but when the glittering 
bauble was almost within their reach, have 
found it suddenly elude their grasp and leave 



194 THE YOU NG MECHANIC. 

them to regret the loss of all which they had 
been toiling for years to acquire. 

Contentment, like every other Christian duty, 
has a great many excellent uses. It is good 
for the mind, for the body, and for the estate 
of every man. It tranquillizes the spirit, it pre- 
serves the health, and it promotes that steady 
economy which leads to competency ; often to 
affluence. The man who is satisfied with the 
position which Providence has assigned him, 
and endeavours to make himself useful in that 
position, presents a vastly more respectable 
figure than one who is constantly struggling to 
place himself in a different position. The fruits 
of this struggle are harassing cares, jealous 
heart-burnings, hazardous enterprises, and often 
debt and ruin. There is an old and homely 
saying, applicable to every one who has been 
brought up to a regular trade or profession — a 
saying full of practical wisdom, which many 
have hitherto disregarded, but which will be 
better observed in years to come — " Keep your 
shop, and your shop will keep you." This 
saying, as 1 have already intimated, is a whole- 
some one for any man who labours for his 
subsistence, whether it be with his head or hit 



KEEP YOUR SHOP. J95 

hands ; but for the mechanic it is the ark of 
safety. 

In some foieign countries it is the custom for 
mechanics to form associations, of which one 
of the leading objects is to retain all the mem- 
bers of each trade in the trade to which he 
belongs. For this purpose they not only aid 
all their brethren who are in distress, but they 
use every exertion to retain within their circle 
all the talent and all the wealth which has 
originated among them. Their public institu- 
tions, libraries and lecture rooms, their scienti- 
fic collections, their pictures and models, afford 
the means of gratifying the most refined taste ; 
and these and the tone which is imparted to 
their circle of society by this noble esprit de 
corps, make it wholly unnecessary for the most 
imbitious person to leave the trade in pursuit 
of any of these objects. Any one may see 
that under such circumstances it is a nobler ob- 
ject of ambition to be highly respected in the 
trade, than can be attained by means of any 
position out of it. The same principle holds 
good under all circumstances. If a man has 
surrounded himself with all the elegancies and 
luxuries which affluence can purchase by dili- 
gence and industry in his trade, he should 
17* 



19g THE YOUNG MECHANIC. 

never a6andon it under the impression that ha 
will thus elevate himself in the estimation of 
his fellow citizens, by putting on a finer coat, 
and appearing in a different character. Such a 
course calls down a torrent of invidious remarks, 
not from his brethren of the trade, who are 
content, for the most part, to regret the deser- 
tion in silence, but the rest of that little world 
by whose Argus eyes the movements of each 
individual in society is watched. On the othei 
hand, the mechanic who remains attached to 
his trade, when it is no longer absolutely ne- 
cessary for his support, is universally respected 
for this mark of steadiness, constancy and good 
sense. In connection with this part of my 
subject, I am strongly reminded of an old ac- 
quaintance of my own, in the old common- 
wealth of Massachusetts, who evidently takes 
an honest pride in his adherence to that trade 
which has long since given him the most ample 
means of luxury and ease. This gentleman is 
referred to by Governor Everett, in one of his 
recent public addresses, in the following terms : 
" I scarce know if I may venture to adduce 
an instance, nearer home, of the most praise- 
worthy and successful cultivation of useful 
knowledge, on the part of an individual with- 



THE ENLIGHTENED MECHANIC. 19/ 

out education, busily employed in mechanical 
industry. I have the pleasure to be acquainted, 
in one of the neighbouring towns, with a 
person, who was brought up to the trade 
of a leather-dresser, and has all his life work- 
ed, and still works, at this business. He has 
devoted his leisure hours, and a portion of 
his honourable earnings, to the cultivation 
of useful and elegant learning. Under the 
same roof, which covers his store and work- 
shop, he has the most excellent library of Eng- 
lish books, for its size, with which I am ac- 
quainted. The books have been selected with 
a good judgment, which would do credit to the 
most accomplished scholar, and have been im- 
ported from England by himself. What is 
more important than having the books, their 
proprietor is well acquainted with their contents. 
Among them are several volumes of the most 
costly and magnificent engravings. Connected 
with his library, is an exceedingly interesting 
series of paintings, in water-colours, which a 
fortunate accident placed in his possession, and 
several valuable pictures, purchased by himself. 
Tin: whole form a treasure of taste and know- 
ledge, not surpassed, if equalled, by any thing 
of its kind in the country." 



d. 



198 THE YOUNG MECHANIC 

Governor Everett might have added thai the 
leading traits in Mr. Bowse's character are 
sound sense and good taste ; and no more de- 
cisive proof of these characteristics could be 
given than his steady adherence to his original 
business. In the same address from which th* 
above paragraph is quoted, the eloquent orator 
urges upon his hearers that every working man 
should cultivate his mind to the utmost of his 
ability ; and he quotes examples of many who 
have thus raised themselves to conspicuous 
offices and honours. I would urge upon all 
working men the same duty of mental cultiva- 
tion, not as affording the opportunity of aban- 
doning their trade; but as giving them the 
means of dignifying and embellishing it. Lo- 
renzo de Medicis by commerce raised his family 
to princely rank — they were the merchant kings 
of their age. The American mechanic has no 
occasion to seek any advancement of this sort, 
for every voter in our country is something 
greater than a king; by virtue of the elective 
franchise he is a maker of kings. When I 
speak of adhering to one's trade, 1 would by 
no means be understood to lay down a rule 
without exceptions. Emergencies may occur 
which shall render it a paramount duty to entei 



DUTY OF WORKING MEN. \ 

upon a new and difficult profession. The me 
chanic, like any other citizen, may be suddenly 
called upon to shoulder his musket and defend 
his country from invasion, as happened in the 
case of General Greene ; or he may be required 
to aid the same great cause by his wisdom in 
council, as in the case of Sherman and Frank 
lin. When a country is to be saved by valour 
or wisdom, it becomes a matter of absolute 
necessity that the working men should contri- 
bute a large contingent towards the grand army 
of defence as well as the council of the nation. 
For a time, at least, a new course of life must 
then be embraced. But the greatest, and most 
celebrated among those who have been detach- 
ed from their trade in this or in any other way, 
have always shown an honest pride in their 
original calling. Girard wrote himself mariner 
in his will ; and Franklin called himself printei 
in his epitaph. 



200 THE YOUNG MECHANIC. 



CHAPTER III. 

THE MECHANIC SHOCJLD HONOUR HIS 
TRADE. 

I have already insisted that the mechanic 
in order to be useful, happy and respectable, 
should become a thorough master of his trade, 
and should remain attached to it. 1 would in 
the next place urge upon him the duty and 
policy which dictate that he should honour his 
trade. There are two ways in which this ma) 7 
be done : first, by seeking distinction in it ; and 
secondly, by adorning it with intellectual re- 
creations. 

The love of distinction is common to nearly 
all men ; and the most remarkable and conspi 
cuous diversities of character are produced by 
the different modes in which this favourite ob 
ject is pursued. One man seeks it by brillian/ 
deeds in the public service, another by munifi 
cent institutions. Here we see distinction 
courted by eloquence, and there by learning 
Some hope to become distinguished by then 
literary efforts, or their scientific discoveries, 
while others, with a less laudable, but not les* 



LOVE OF DISTINCTION 2(h 

aniesl ambition, seek to attract public atten- 
tion by mere eccentricity of character or extra- 
vagance in conduct, dress or equipage. Doubt- 
less this passion, so generally prevalent among 
men, has been implanted in the human breast 
for a wise and useful purpose ; and it is there- 
fore right to allow it a field for action, provided 
that field be a safe and honourable one. If this 
postulate be granted, I would ask what could 
afford a fairer and nobler field for any man's 
ambition, than the pursuit of distinction by ex- 
traordinary excellence in his trade or profes- 
sion. Each of the mechanical trades affords 
ample room for the exercise of ingenuity in 
the improvement of its processes, and the con- 
sequent improvement of its products ; and the 
free institutions and abundant resources of our 
country, and the ease with which the workman 
may support himself, has already enabled Ame- 
rican industry and invention in many instances 
to claim the admiration of the world. It must 
be a proud reflection to the American mechanic, 
that one of his class has exacted the most un- 
equivocal homage to the genius of our country 
from the proud Sultan of the East, by his won- 
derful skill as a naval constructor; and every 
Philadelphian may justly entertain a feeling o\ 



202 THE YOUNG MECHANIC 

exultation when he remembers that a mechanic 
of one of our cities is at this moment furnishing 
locomotive engines, acknowledged to be supe- 
rior to all others, for the use of British and 
Austrian rail road companies. Such distinction 
as this we must acknowledge to be fairly and 
honourably won. It is true that all may not 
hope to rise so high in the world's estimation 
as to attract applause from foreign countries. 
But every one may reap the reward of diligence, 
ingenuity and devotion to his business, in the 
applause of that valued circle, Vhich is, in a 
certain sense, all the world to him — the circle 
of his associates and friends. 

Again, the mechanic may honour his trade 
by adorning it with intellectual recreations. It 
is not desirable, in fact it is not possible for a 
man to devote every moment of his time to the 
business by which he lives. Such intense ap- 
plication is injurious both to the body and the 
mind. It destroys health, racks the brain, and 
ruins the temper. The repose of the domestic 
circle, the quiet hour for reading or music, ot 
relaxation of some other kind, seems absolutely 
necessary for the preservation of that greatest 
of earthly blessings — a sound mind in a healthy 
body. The business of the mechanic is pre* 



EXAMPLE OF CHARLES LAMB. 



203 



eisely that which renders it most expedient foi 
him to give his recreations an intellectual cast ; 
and it is owing to the circumstance that the 
alternation of mental and bodily labour is best 
suited to the human constitution, that some of 
the most beautiful and brilliant productions of 
the human intellect have proceeded from those 
persons who were compelled, for many hours 
of each day, to labour at a business which was 
purely mechanical. Cast your eye over the 
whole field of English literature, and see who 
it is that has brought the art of essay writing 
to its greatest perfection. Of course you in- 
stantly answer, Charles Lamb. He is univer- 
sally acknowledged to be in this department 
inimitable, unrivalled, unapproachable. The 
best critics say that we can never hope to see 
such essays produced by any other writer. 
Yet these beautiful productions were the work 
of leisure evenings. The composition of them 
served as a relaxation, after severe labour 
through the day at the India House in copy- 
ing commercial papers, which to him must have 
been a perfectly mechanical operation. Never- 
theless, he had the good sense to adhere to this, 
his trade, long after he was one of the most 
famous writers in Kngland, and in fact until hi* 
IS 



204 THE YOUNG MECHANIC. 

age and services entitled him to a retiring pen 
sion. I will not weary your patience by citing 
other examples, although there are thousands at 
hand, in proof of my position that intellectual 
recreations are particularly appropriate for the 
mechanic, and that they form the proper and 
legitimate ornament of his trade. 

Coleridge, an author by profession, tells* us 
in plain terms that it is necessary, in order to 
be successful in works of imagination, to have 
some profession or trade which is to a certain 
extent mechanical, and he affectionately exhorts 
all young people to avoid his own profession 
if they would be useful and happy. I cite his 
observations, which are as remarkable as they 
are just. 

u An interest in the welfare of those who, at 
the present time, may be in circumstances not 
dissimilar to my own at my rirst entrance into 
life, has been the constant accompaniment, and, 
(as it were,) the under-song of all my feelings. 
Whitehead, exerting the prerogative of his lau- 
reateship, addressed to youthful poets a poetic 
charge, which is perhaps the best, and certainly 
the most interesting of his works. With no 
other privilege than that of sympathy and sin- 
cere good wishes. I would address an affectionate 



TRADE OF AUTHORSHIP. 20b 

exhortation to the youthful literati, grounded on 
my own experience. Jt will be but short; for 
the beginning, middle, and end, converge to one 
charge: Never pursue literature as a trade. 
With the exception of one extraordinary man, I 
have never known an individual, least of all, an 
individual of genius, healthy or happy without 
a profession, i. e. some regular employment 
which does not depend on the will of the mo- 
ment, and which can be carried on so far me- 
chanically, that an average quantum only of 
health, spirits, and intellectual exertion, are 
requisite to its faithful discharge. Three hours 
of leisure, unannoyed by any alien anxiety, 
and looked forward to with a delight as a 
change and recreation, will suffice to realize in 
literature, a larger product of what is truly 
genial, than weeks of compulsion. Money and 
immediate reputation, form only an arbitrary 
and accidental end of literary labour. The 
hope of increasing them, by any given exertion, 
will often prove a stimulant to industry ; but 
the necessity of acquiring them will, in all 
works of genius, convert the stimulant into a 
narcotic. Motives by excess reverse their very 
nature, and, instead of exciting, stun and stu- 
pify the mind. For it is one contradistinction 



206 THE YOUNG MECHANIC. 

of genius from talent, that its predominant 
end is always compromised in the means ; and 
this is one of the many points which establish 
an analogy between genius and virtue. Now, 
though talents may exist without genius, yet, 
as genius cannot exist, certainly not manifest 
itself, without talents, I would advise every 
scholar who feels the genial power working 
within him, so far to make a division between 
the two, that he should devote his talents to 
the acquirement of competence in some known 
trade or profession, and his genius to objects 
of his tranquil and unbiassed choice ; while fl\u 
consciousness of being actuated in both alike 
by the sincere desire to perform his duty, will 
alike ennoble both. My dear young friend, (I 
would say,) ' suppose yourself established in 
any honourable occupation. From the manu- 
factory, or counting-house, from the law court, 
or from having visited your last patient, you 
return at evening — 

Dear tranquil time, when the sweet sense of home 
Is sweetest — 

to your family, prepared for its social enjoy- 
ments, with the very countenances of your wife 
and children brightened, and their voice ol 
welcome made doubly welcome by the know- 



TRADE OF AUTHORSHIP. 20? 

ledge that, as far as they are concerned, you 
have satisfied the demands of the day, by the 
labour of the day. Then when you retire into 
your study, in the books on your shelves you 
revisit so many venerable friends with whom 
you can converse. Your own spirit, scarcely 
less free from personal anxieties than the great 
minds that, in those books, are still living for 
you ! Even your writing desk with its blank 
paper, and all its other implements, will appear 
as a chain of flowers, capable of linking your 
feelings, as well as thoughts, to events and cha- 
racters past or to come ; not a chain of iron, 
which binds you down to think of the future, 
and the remote, by recalling the claims and 
feelings of the preremptory present. But why 
should F say retire f The habits of active life 
and daily intercourse with the stir of the world, 
will tend to give you such self-command, that 
the presence of your family will be no inter- 
ruption. Nay, the social silence or undisturb- 
ing voices of a wife or sister, will be like a 
restorative atmosphere, or soft music, which 
moulds a dream without becoming its object 
If facts are required, to prove the possibility of 
combining weighty performances in literature 
with lull and independent employment, the 
16* 



208 



THE VOTING MECHANIC. 



works of Cicero and Xenophon among the 
ancients, of Sir Thomas More, Bacon, Baxter, 
or, to refer, at once, to later and contemporary 
instances, Darwin and Roscoe, are at once dec i- 
sive of the question. 

" Whatever be the profession or trade chosen, 
the advantages are many and important, com- 
pared with the state of a mere literary man, 
who, in any degree, depends on the sale of his 
works for the necessaries and comforts of life. 
In the former, a man lives in sympathy with 
the world in which he lives. At least, he ac- 
quires a better and quicker tact for the know- 
ledge of that with which men in general can 
sympathize. He learns to manage his genius 
more prudently and efficaciously. His powers 
and acquirements gain him likewise more real 
admiration, for they surpass the legitimate ex- 
pectation of others. He is something besides 
an author and is not therefore considered 
merely as an author. The hearts of men are 
open to him, as to one of their own class ; and 
whether h^ exerts himself or not in the con 
versational circles of his acquaintance, his 
silence is not attributed to pride, nor his com- 
municativeness to vanity. To these advantages 
I will venture tc add a superior chance of hap- 



TRADE OF AUTHORSHIP. 20*b 

piness in domestic life, were it only that it is as 
natural for the man to be out of the circle of 
his household during the day, as it is merito- 
rious for the woman to remain for the most 
part within it. But this subject involves points 
of consideration so numerous and so delicate, 
and would not only permit, but require such 
ample documents from the biography of literary 
men, that I now merely allude to it in transitu. 
When the same circumstance has occurred at 
very different times to very different persons, 
ill of whom have some one thing in common, 
there is reason to suppose that such circum- 
stance is not merely attributable to the persons 
concerned, but is in some measure occasion- 
ed by the one point in common to them all. 
Instead of the vehement and almost slanderous 
dehortation from marriage, which the ' Miso- 
gyne Boccaccio' ( Vita e Costumi di Dante, p. 
12. 16) addresses to literary men, 1 would 
substitute the simple advice : be not merely a 
man of letters ! Let literature be an honour- 
able augmentation to your arms, but not con- 
stitute the coat, or fill the escutcheon ! 

" It would be a s->rt of irreligion, and scarce- 
ly less than a libel on human nature, to believe 
that there is any established and reputable pro- 



210 THE YOUNG MECHANIC. 

fession or employment, in which a man niaj 
not continue to act with honesty and honour ; 
and, doubtless, there is likewise none which 
may not at times present temptations to the 
contrary. But wofully will that man find him- 
self mistaken, who imagines that the profession 
of literature, or (to speak more plainly) the 
trade of authorship, besets its members with 
fewer or with less insidious temptations, than 
the church, the law, or the different branches 
of commerce.' " 

Charles Lamb himself subscribes to this 
opinion of Coleridge, and urges it upon one of 
his friends with great force ; and Herder is 
quoted by Coleridge in support of his own 
opinion, as follows : 

Translation. — " With the greatest possible 
solicitude avoid authorship. Too early, or im- 
moderately employed, it makes the head waste 
and the heart empty, even were there no other 
worse consequences. A person who reads only 
to print, in all probability reads amiss ; and he 
who sends away through the pen and the press, 
every thought, the moment it occurs to him, 
will in a short time have sent all away, and 
will become a mere journeyman of the printing 
office, a compositor." 






NECESSITY OF A TRADE. 



L>1 



So much for the opinion of great authors on 
rt.e character of their trade. 

In all these observations you find it distinctly 
admitted that the fancy, the imagination, the 
creative powers of the mind are not to be taxed 
for the purposes of mere support. They say 
it is better to work for a living at some business 
which is mechanical, by way of a regular trade 
or profession, and to give the genius free pky 
in the hours of recreation. That such a dis- 
tribution of one's time may produce the hap- 
piest effect is abundantly apparent from the 
experience of all ages. Without adverting to 
the busy life led by Cicero and Quinctilian, 
whom I esteem among the best authors of an- 
cient times, we may come down at once to the 
moderns. Bacon, the prince of philosophers, 
was a lawyer laboriously active in his profes- 
sion during the greater part of his life ; Shaks- 
peare, the most admirable of all writers, was a 
player and manager, and was obliged to work 
hard at the mechanical part of these laborious 
employments ; Raleigh was a soldier and states- 
man, one of the most active of his age ; Cla- 
rendon was a busy statesman and lawyer; Addi- 
son was secretary of state while he .vas writing 
the Spectator; Walter Scott was a writer for 



212 THE YOUNG MECHANIC 

the signet, and sheriff of the county ; and it i9 
a curious fact that this writei, the most prolific 
as well as the best of our century, passed his 
days in bodily labour, riding about the county 
or working at his profession. It was remarked 
that nobody could conjecture when it was that 
he found time to write his voluminous works. 

If we come to our own country, the exam- 
ples are more numerous. All our best authors 
are working men. Prescott is a lawyer ; Ban- 
croft, a teacher for some years, and afterwards 
collector of the port of Boston ; Charles Sprague 
is a bank clerk ; Halleck collects Mr. Astor's 
rents ; Dana is a lawyer; Longfellow, a teacher. 
In fact, with us, authorship is seldom a profes- 
sion. Most of our literature has been produced 
in the leisure hours rescued from laborious oc- 
cupations. 

Our scientific and useful inventions too have 
generally resulted from the very course which 
I am desirous to recommend to the mechanic, 
viz. : that of honouring his trade by adorning 
it with intellectual recreations. Fulton was a 
portrait painter, who amused himself in his idle 
hours with experiments on steam power ; Whit- 
ney, the inventor of the cotton gin, was a ma- 
chinist, whose judicious employment of his 



AMERICAN AUTHORS. 215 

leisure moments led him to an invention which 
has trebled the value of cotton lands at the 
South ; Whittemore, of West Cambridge, who 
invented the machinery for the manufacture of 
cards, was, if 1 recollect right, a cabinet maker.. 
The case of Franklin is familiar to all. 

All these examples tend to establish the same 
truth, — that a mechanical business, a life of acti- 
vity and labour, is far from being unfavourable 
to the highest operations of the intellect; and 
that relaxation from active labours is most ap- 
propriately found in mental recreation*. 



L 



214 THE YOUNG MECHANIC. 



CHAPTER IV 

THE MECHANIC SHOULD DEVOTE HIS LEI- 
SURE TO THE GENERAL INTERESTS OF 
HIS TRADE. # 

One more duty I would urge upon the me- 
chanic, in order to the finishing of his charac- 
ter of a useful, happy and respectable man. 
Having attained wealth at the time of life when 
it is desirable to cease from active labour, I 
would have him devote himself to the genera 
interests of his trade. 

There are many ways in which the wealthy 
mechanic may promote the general interests of 
his trade, when he has retired from all partici- 
pation in its labours or profits. 

He may give a tone to its society by exer- 
cising a refined and judicious hospitality. Ht 
may make his house the resort of kindred spi- 
rits, who will unite with him in their endeavours 
to retain men of talent and influence in the 
trade. He may assist young men who are en- 
teiing upon business for themselves with money, 
credit and good advice. He may save many a 
br >ther from ruin by interposing a friendlv 



FRANKLIN. 215 

voice, and a helping hand at the critical moment 
when they are most needed. He may become 
in his old age the Mecaenas, as well as the 
Nestor of his fraternity, by patronizing the in- 
tellectual efforts of their leisure hours. 

Such was the course of Franklin ; and his 
munificent aid ceased not with his life. In his 
will a permanent fund was established for aiding 
the young mechanics of his native place by loans 
of money. The example of his life, however, 
has been of more value than a legacy of millions. 
He was a mechanic who fulfilled the several 
conditions which we have been considering as 
necessary to happiness, usefulness and respect- 
ability. He made himself a thorough master 
of his trade ; he adhered to it till the impera- 
tive call of his suffering country compelled him 
to relinquish it; and he honoured his trade by 
seeking distinction in it, and by adorning it 
with intellectual recreations. Long may his 
example be imitated by his countrymen — long 
may his race live and flourish in the land. 
Such mechanics are the bulwark of our free 
institutions. While we have men of the Frank- 
lin stamp among us, we shall never want a 
supply of heroes and statesmen to perform great 
and brilliant actions, or poets, historians and 

orators to celebrate them. 
19 



216 THE YOUNG MECHANIC. 



CHAPTER V. 

MISDIRECTION OF INDUSTRY— PREJUDICES 
AGAINST THE MECHANICAL TRADES. 

Among the many causes which have led t . 
the present depressed state of affairs in 0111 
country, there is one which appears to me an 
efficient one, although it has been in a great 
measure overlooked. This is the misdirection 
of industry — of productive labour. All obser- 
vers readily perceive that capital has been 
thrown away ; few take notice of the fact tliat 
hands and heads have been employed on works 
that are now known to be utterly useless. 
Railroads, for example, have been constructed, 
which can never, by any possibility, be re- 
quired for the public accommodation to such 
an extent as to pay the expense of keeping 
them in repair and employing lines of cars 
upon them. Mines have been opened and 
wrought in situations where no veins of metal 
existed, although the imaginations of the stork- 
holders, aided by the fine stories of some cun- 
ning Dousterswivel, had made each of the re 



MISAPPLICATION OF TIME AND TALENTS. OJ7 

fious a perfect El Dorado. Even agriculture 
labour has been misapplied ; for trees have been 
planted and nursed with the greatest care, un- 
der the impression that their leaves were to be 
converted into silks which should rival the 
fabrics of Lyons and Benares ; and yet these 
very trees have subsequently been cut down as 
cumberers of the ground. 

The productive industry of this country migh 
just as well have been employed in the con 
stmction of pyramids, like those of the ancient 
Egyptians, as on works of this nature. It is 
literally labour, time, and talents thrown away. 

But these are not the only ways in which 
labour, time and talent have been misdirected. 
Thousands of our young men have entered the 
learned professions when they were already 
crowded, and are consequently wasting their 
lives in vain hopes; and other thousands have 
devoted themselves to the pursuits of com- 
merce without capital, prudence, or intelligence 
sufficient to avoid the dangers of commercial 
enterprize ; and these men are now either bank- 
rupts, or involved in a series of embarrassments 
vvhich may last through their whole lives. An 
error in the choice of one's profession is one 
which a followed by painful consequences, as 



21S 



THE, YOUNG MECHANIC. 



many have found to their cost. In this coun- 
try we are apt to be too ambitious and restless. 
The freedom of our institutions, instead of im- 
pressing upon us the wholesome lesson that ail 
men are naturally equal in dignity, and that 
consequently every trade and profession may 
be ennobled by the personal merit of its mem- 
bers, leads men to aspire to certain professions 
which they esteem genteel ; and to high oflices 
which the constitution has made attainable by 
citizens of all classes. 

This is wrong. An American should respect 
himself. A citizen of this republic should deem 
himself a peer of the world — one of nature's 
noblemen. He should consider that the cir- 
cumstance of his being an American citizen is 
sufficient to adorn with all proper dignity any 
trade or profession which he may adopt. 
Having settled this point with himself, he is 
left at perfect liberty to look around with an 
unprejudiced mind, upon the different modes 
of obtaining subsistence and making himself 
useful to the community ; and he can make his 
choice upon the same principles that should 
govern him in deciding any practical question. 
In taking a survey of some large community 
with reference to the success which has aUend 



MECHANICS AND MERCHANTS. 219 

$(] the exertions of other men, in order to aid 
his judgment in the choice of a profession, the 
youth or his adviser may peradventure, arrive 
at some results which he did not anticipate. 

Suppose, for example, that he should examine 
the comparative success of those men whom 
we know to have devoted themselves to me- 
chanical trades, and those who have become 
merchants. Would it not be apparent that where 
one mechanic has failed and caused extensive 
losses to his friends and the community, ten 
merchants have done the same thing ? On the 
other hand, would it not appear that where one 
merchant had acquired a competent fortune and 
retired from business in the decline of life, se- 
veral mechanics have done the same thing? If 
we were to run over the list of persons taxed 
for real estate, should we not find more me- 
chanics than merchants living in their own 
houses, and deriving a handsome income from 
tl^eir rents r 

If it be said that this not a fair test of com- 
parative success, let another be resorted to 
Take the whole number of persons employed 
in mechanical trades, and the whole number of 
persons employed in commerce, say for the last 
twenty years; then calculate what per centals 
19* 



*>20 TIIE YOUNG MECHANIC. 

of each class lias failed, what per centage hris 
gained a decent subsistence without failing. ano 
what per centage has arrived at what is called 
independence. The result of such an inquiry 
would satisfy the inquirer that it is a safei 
course to become a mechanic than to be a 
merchant. 

The prejudice against the mechanical trades 
is a relic of feudalism unworthy of our free 
country. Considered with reference to those 
old feudal prejudices, all the pursuits by which 
bread is earned in our country are equally 
base. Considered in the light of republican 
philosophy, they are all equally honourable. 
The baron of the middle ages, who could not 
read or write, looked down upon the merchant, 
the mechanic, and the lawyer with equal con- 
tempt ; and the baron of modern days, who 
cannot even wield a lance, considers himself 
superior to the greatest, wisest, and best of 
those who were born commoners. These old 
feudal prejudices are ridiculous. But when we 
call one profession respectable^ and another 
less respectable, do we not adopt them ? When 
we talk of degrading ourselves by making 
tradesmen of our sons, do we not give sanc- 
tion to the stupid and exploded notions of the 



FEUDAL PREJUDICES. 



221 



' dark ages ? When we admit that any citizen 
may lose caste by associating with any other 
honest and honourable man, do we not submit 
to a barbarism worse than Gothic — the bar- 
barism of Hindostan and China ? 

Such notions should be laid aside witli other 
useless lumber, as unlit for an age and a coun- 
try where common sense gives law to society, 
nd where real merit stamps the seal of respect- 
ability. It is but fighting shadows to offer ar- 
guments in opposition to such views. I gladly 
turn therefore from this to the more agreeable 
task of continuing the subject of my last lec- 
ture — the mechanic. 



222 TIIE YOUNG MECHANIC. 



CHAPTER VI. 

INTELLECTUAL CULTIVATION OF THE 
MECHANIC— ITS IMPORTANCE. 

I propose now to offer a few remarks on the 
intellectual cultivation of the mechanic, its im- 
portance, its means, and its rewards. 

That intellectual cultivation, as a means of 
moral and social elevation, is as important to 
the mechanic as it is to any other citizen, is a 
truth so obvious as not to require argument or 
illustration for its support. But this is not all 
He has stronger reasons for study than most 
other men. His very livelihood may depend 
in a great measure on a degree of skill in his 
art which cannot be acquired without a know- 
ledge of the scientific principles and natural 
laws on which the arts are founded. 

The whole system of mechanics' institutes, 
lyceums, lectures, and collections of specimens 
and machines, is nothing more nor less than an 
open confession made by the mechanics them- 
selves, that intellectual cultivation has become 
absolutely necessary, in order that they maf 



COMPETITION. 



22^ 



keep pace with the spirit of the age — an ac- 
knowledgment that the time has come when 
science and art shall be firmly united, and this 
head and the hands shall work together. 

Competition imposes upon the mechanic oi 
the present day the necessity of study. Unless 
he keeps pace with the intelligence of the times, 
he will speedily find himself working at a 
ruinous disadvantage. While the workman 
who is content to remain stationary in scien 
tific intelligence, neglects the opportunities of 
information afforded by the institute, the read- 
ing room, and a constant social intercourse 
with the most intelligent of his trade; his 
neighbour, availing himself of these advantages, 
may possess himself of new processes, new 
materials, or new facts, which will enable hire 
to reduce his prices, and in a great measure tc 
carry off the custom of the place. 

It was not always thus. Monopoly and pre- 
scription formerly exerted an influence as inju- 
rious to the arts as that which is now exerted 
by competition is beneficial. 

Indeed, as has been ably shown by a learned 
authority,* much mischief has been occasioned 



Governor Everett. Oration, p. 232. 



224 TIIE tfOUNG MECHANIC. 

in past times by the ignorance of artizans lie 
says : — 

"The history of the progress oi the human 
mind shows us, that for want of a d illusion 
of scientific knowledge among practical men, 
great evils have resulted, both to science and 
practice. Before the invention of the art of 
printing, the means of acquiring and circulating 
knowledge were few and ineffectual. The phi- 
losopher was, in consequence, exclusively a 
man of study, who, by living in a monastic 
seclusion, and by delving into the few books 
which time had spared, — particularly the works 
of Aristotle and his commentators, — succeeded 
in mastering the learning of the day ; learning, 
mostly of an abstract and metaphysical nature. 
Thus, living in a world not of practice, but 
speculation, never bringing his theories to the 
vest of observation, his studies assumed a vi- 
sionary character. Hence the projects for the 
transmutation of metals ; a nation not origi- 
nating in any observation of the qualities ol 
the different kinds of metals, but in reasoning 
i priori, on their supposed identity of sub 
stance. " So deep rooted was this delusion, thai 
\ great part of the natural science of the mid- 
dle ages consisted in projects to convert th« 



EVILS OF IGNORANCE. 



22A 



baser metals into gold. It is plain, that such a 
project would no more have been countenances 
by intelligent, well-informed persons, pracfi- 
rally conversant with the nature of the metals, 
than a project to transmute pine into oak, or 
fish into flesh. 

" In like manner, by giving science wholly 
up to the philosophers, and making the practical 
arts of life merely a matter of traditionary repel i- 
tion from one generation to another of uninform- 
ed artists, much evil of an opposite kind was 
occasioned. Accident, of course, could be the 
only source of improvement ; and for want of 
acquaintance with the leading principles of 
mechanical philosophy, the chances were inde- 
finitely multiplied against these accidental im- 
provements. For want of the diffusion of in 
formation among practical men, the principles 
prevailing in an art in one place were unknown 
in other places *j and processes existing at one 
period were liable to be forgotten in the lapse 
of time. Secrets and mysteries, easily kept in 
such a state of things, and cherished by their 
possessor as a source of monopoly, were so 
common, that mystery is still occasionally usee 
as synonymous with trade. This also contri- 
buted to the loss of arts once brought to per 



226 THE ^OUNG MECHANIC 

fe^tion, such as that of staining glass, as prac- 
tised in the middle ages. Complicated inn- 
chinery was out of the question ; for it requites, 
for its invention and improvement, the union of 
scientific knowledge and practical skill. The 
manner was left to creep along the coast, while 
the astronomer was casting nativities ; and the 
miner was reduced to the most laborious and 
purely mechanical processes, to extract the 
precious metals from the ores that really con- 
tained them, while the chemist, who ought to 
have taught him the method of amalgamation, 
could find no use for mercury, but as a men- 
struum, by which baser metals could be turned 
into gold. 

" At the present day, this state of things is 
certainly changed. A variety of popular trea- 
tises and works of reference have made the 
great principles of natural science generally 
accessible. It certainly is in the power of al- 
most every one, by pains and time properly 
bestowed, to acquire a decent knowledge ol 
every branch of practical philosophy. But 
still, it would appear, that, even now, this part 
of education is not on the right footing. Gene- 
rally speaking, even now, all actual instruction 
in the principles of natural science is confined 



EDUCATION OF MECHANICS. 22> 

to the colleges ; and the colleges are, for the 
most part, frequented only by those intended 
for professional life. The elementary know- 
ledge of science which is communicated at the 
colleges, is indeed useful in any and every 
calling ; but it does not seem right that none 
but those intended for the pulpit, the bar, or 
the profession of medicine, should receive in- 
struction in those principles which regulate the 
operation of the mechanical powers, and lie 
at the foundation of complicated machinery; 
which relate to the navigation of the seas, the 
smelting and refining of metals, the composi 
tion and improvement of soils, the reduction 
to a uniform whiteness of the vegetable fibre, 
the mixture and application of colours, the 
motion and pressure of fluids in large masses, 
the nature of light and heat, the laws of mag- 
netism, electricity, and galvanism. It would 
seem that this kind of knowledge was more 
immediately requisite for those who are to con- 
struct or make use of labour-saving machinery, 
who are to traverse the ocean, to lay out and 
direct the excavation of canals, to build steam 
engines and hydraulic presses, to work mines, 
and to conduct large agricultural and manufac 
String establishments. Hitherto, with somt 
20 



228 THE YOUNG MECHANIC. 

partial exceptions, little has been done, syste. 
matically, to afford to those engaged in those 
pursuits, that knowledge which, however con* 
venient to others, would seem essential to them. 
There has been scarce any thing, which could 
be called education for practical life ; and those 
persons who, in the pursuit of any of the use 
ful arts, have signalized themselves by the em 
ployment of scientific principles for the inven- 
tion of new processes, or the improvement of 
the old, have been self-educated men." 

It is argued, in opposition to this view of the 
matter, that the greatest discoveries and inven- 
tions have Deen produced by self-taught men, 
or by accidental circumstances, and that educa- 
tion is therefore unnecessary for the mechanic. 
The fact, is indisputable ; but the argument 
founded on it against the intellectual cultiva- 
tion of working men, is not sound. Another 
fact will sufficiently refute it. Before education 
became generally diffused among mechanics, 
useful discoveries and inventions were much 
rarer Uan they are at present. When the great 
mass of mechanics could neither read nor write, 
the progress of invention was exceedingly 
Blow. Now it is astonishingly rapid. In the 
middle ages great discoveries in the arts wer« 



A LIFE OF LABOUR. 229 

made at the rate of about one in a hundred 
years. Now they are made almost every year. 
Within the range of our own recollection two 
great motive powers, unknown before, have 
been rendered available in the arts of life, and 
scarcely a month passes without the announce- 
ment of some new contrivance for economizing 
the labour of man. This fact not only an- 
swers the argument already cited, but acts with 
tremendous power on the opposite side : thus, 

The increase of education among mechanics 
increases the number of discoveries and im- 
provements in the arts, by which human labour 
is abridged. This increase of power is an in- 
crease of happiness. It elevates the mechanic 
in the scale of social being, and adds to the 
comfort — the essential happiness of society. 
By means of the recent improvements in the 
arts effected by ingenious and educated mecha- 
nics, the amount of severe bodily labour pre- 
viously imposed on that class of men is greatly 
diminished ; and this is no small gain. 

" We read," says a shrewd writer, u we read 
in many authors great encomiums on a life of 
labour, and of the superior blessings of peasants 
and hard-working men, whose temperate and 
abstemious lives n rt .mly make them enjoy an 



230 THE YOUNG MEChAWlC. 

uninterrupted state of health, but throw a 
crimson on their cheeks, and give a vigour to 
their bodies, the sons of wealth and affluence, 
they tell us, may in vain sigh for. This sounds 
well ; but I own I am doubtful of the fact 

" If I compare the working part of mankind, 
who fare hard, with those who eat and drink 
of the i good things of the earth,' I think I can 
discern better complexions, choicer animal spi- 
rits, and stronger bodies in the latter than in 
the former. Incessant labour and coarse and 
scanty food, have certainly a tendency to weaken 
the bodies of mankind, and wear them out be- 
fore their time ; and this we see is the case. 
What becomes then of the fine-spun theories 
of visionary authors who so greatly extol a 
laborious life ? Why, they are destroyed, like 
other cobweb systems, that will not bear hand- 
ling." 

Education multiplies the inventions which 
lighten bodily labour. Education among me- 
chanics is, therefore, a great blessing ; and it 
should be a settled policy with this large and 
influential class of citizens, to encourage in 
every possible way the intellectual cultivation 
of all who compose their body. 

The kind of education which is suitable for 



APPLICATION OF SCIENCE TO ART. 231 

b mechanic is that which is best accommodated 
to his circumstances. It should be liberal, — 
not minute. To learn the practical application 
of every science to every art, is not in the 
power of any single individual ; but the me- 
chanic, as well as the professed scholar, may 
learn the general laws and principles of science; 
and subsequently carry out to any degree which 
may seem expedient for him, those details which 
are particularly applicable to his own trade. 
His general acquaintance with the physical laws 
will enlarge his sphere of usefulness, and in- 
crease his chances of success in any particular 
art. 

There are many good reasons why the Ame- 
rican mechanics, more than those of any other 
nation, should cultivate science. One reason 
of this is the exalted station in society which 
he enjoys here, compared with that assigned to 
the same class of men in other countries. 

In this connexion, I will again quote the au- 
thority of Governor Everett. 

And first, he says, it is beyond all ques- 
tion, that what are called the mechanical trader 
of this country are on a much more liberal 
footing than they are in Europe. This circum- 
stance not only ought to encourage those whe 
20* 



232 THE YOUNG MECHANIC. 

pursue them, to take an honest pride in im 
provernent, but it makes it their incumbent duty 
to do so. In almost every country of Europe, 
various restraints are imposed on the mecha- 
nics, which almost amount to slavery. A good 
deal of censure has been lately thrown on the 
journeymen printers of Paris, for entering into 
combinations not to. work for their employers, 
and for breaking up the power presses, which 
were used by the great employing printers. 1 
certainly shall not undertake to justify any acts 
of illegal violence, and the destruction of pro- 
perty. But when you consider that no man 
can be a master printer in France without a 
license, and that only eighty licenses were 
granted in Paris, it is by no means wonderful 
that the journeymen, forbidden by law to set 
up for themselves, and prevented by the power 
presses from getting work from others, should 
be disposed, after having carried through one 
revolution for the government, to undertake 
another for themselves. Of what consequence 
is it to a man, forbidden by the law to work 
for his living, whether Charles X. or Louis 
Philip is king ? 

In England, it is exceedingly difficult tor a 
mechanic to obtain a settlement in *pv town 



CONDITION OF FOREIGN MECHANICS. 23^ 

except that in which he was born, or where he 
served his apprenticeship. The object of impos- 
ing these restrictions is, of course, to enforce on 
each parish the maintenance of its native poor ; 
and the resort of mechanics from place to place 
is permitted only on conditions with which 
many of them are unable to comply. The con- 
sequence is, they are obliged to stay where they 
were born ; where, perhaps, there are already 
more hands than can find work ; and, from the 
decline of the place, even the established arti- 
sans want employment. Chained to such a spot, 
where chance and necessity have bound him, the 
young man feels himself but half free. He is 
thwarted in his choice of a pursuit for life, and 
obliged to take up with an employment against 
his preference, because there is no opening in any 
other. He is depressed in his own estimation, 
because he finds himself unprotected in society. 
The least evil likely to befall him is, that he 
drags along a discouraged and unproductive 
existence. He more naturally falls into dissi- 
pation and vice, or enlists in the army or navy ; 
while the place of his nativity is gradually be- 
coming a decayed, and finally a rotten borough, 
and, as such, enables some rich nobleman to 



234 THE YOUNG MECHANIC. 

send two members to parliament, to make laws 
against combinations of wcrkmen. 

In other countries singular institutions exist, 
imposing oppressive burdens on the mechanical 
classes. 1 refer now more particularly to the 
corporations, guilds, or crafts, as they are called, 
that is, to the companies formed by the mem- 
bers of a particular trade. These exist, with 
great privileges, in every part of Europe ; in 
Germany, there are some features in the insti- 
tution, as it seems to me, peculiarly oppressive. 
The different crafts in that country are incor- 
porations recognized by law, governed by 
usages of great antiquity, with funds to defray 
the corporate expenses, and in each consider- 
able town, a house of entertainment is selected, 
as the house of call (or harbour, as it is styled,) 
of each particular craft. No one is allowed to 
set up as a master workman, in any trade, un- 
less he is admitted as a freeman, or member of 
the craft ; and such is the stationary condition 
of most parts of Germany, that I understand 
that no person is admitted as a master work- 
man in any trade, except to supply the place 
©f some one deceased or retired from business. 
When such a vacancy occurs, all those desirous 
of being permitted to nil it, present a piece of 



CONDITION OF FOREIGN MECHANICS. O;^ 

work, which is called their master-piece, bei»>g 
offered to obtain the place of a master work- 
man. Nominally, the best workman gets the 
place; but you will easily conceive, that, in 
reality, some kind of favouritism must generally 
decide it. Thus is every man obliged to sub- 
mit to ail the chances of a popular election, 
whether he shall be allowed to work for his 
bread ; and that too, in a country where the 
people are not permitted to have any agency in 
choosing their rulers. But the restraints od 
journeymen, in that country, are still more op- 
pressive. As soon as the years of apprentice- 
ship have expired the young mechanic is 
obliged, in the phrase of the country, to wander 
for three years. For this purpose he is furnish- 
ed by the master of the craft in which he has 
served his apprenticeship, with a duly authen- 
ticated wandering book, with which he goes 
forth to seek employment. In whatever city 
he arrives, on presenting himself, with this cre- 
dential, at the house of call, or harbour, of the 
craft in which he has served his time, he is al- 
lowed, gratis, a day's food and a night's lodging. 
If he wishes to get employment in that place, 
he is assisted in procuring it. If he does not 



236 TIIE YOUNG MECHANIC 

wish to, or fails in the attempt, he must pursue 
his wandering ; and this lasts for three years, 
before he can be any where admitted as a mas- 
ter. I have heard it argued, that this system 
had the advantage of circulating knowledge 
from place to place, and imparting to the young 
artisan the fruits of travel and intercourse with 
the world. But however beneficial travelling 
may be, when undertaken by those who have 
the capacity to profit by it, I cannot but think 
that to compel every young man, who has just 
served out his time, to leave his home, in the 
manner I have described, must bring his habits 
and morals into peril, and be regarded rathei as 
a hardship than as an advantage. There is no 
sanctuary of virtue like home. 

You will see, from these few hints, the na- 
ture of some of the restraints and oppressions 
to which the mechanical industry of Europe is 
subjected. Wherever governments and corpo- 
rations thus interfere with private industry, the 
spring of personal enterprise is unbent. Men 
are depressed with a consciousness of living 
under control. They cease to feel a respon- 
sibility for themselves, and, encountering ob- 
stacles whenever they step from the beaten path, 
they give up improvement as hopeless. I netiJ 



CONDITION OF FOREIUN MECHANICS. 23"; 

not remark on the total difference of tilings m 
America. We are apt to think, that the only thing 
in which we have improved on other countries, 
is our political constitution, whereby we choose 
our rulers, instead of recognizing their heredi- 
tary rights. But a mi ch more important differ- 
ence between us an I foreign countries is 
wrought into the very texture of our society ; 
it is that generally pervading freedom from re- 
straint, in matters like those I have just speci- 
fied. In England, it is said that forty days 
undisturbed residence in a parish gives a jour- 
neyman mechanic a settlement, and consequent- 
ly entitles him, should he need it, to support 
from the poor rates of that parish. To obviate 
this effect, the magistrates are on the alert, and 
instantly r q,el a new comer from their limits, 
who d' js not possess means of giving security, 
such as few young mechanics command. A 
duress like this, environing the young man, on 
his entering into life, upon every side, and con- 
demning him to imprisonment for life on the 
spot where he was born, converts the govern- 
ment of the country, — whatever be its name,— - 
into a despotism. 

Such is the condition of mechanics abroad ; 
web, thanks to our free institutions and the 



238 THE YOUNG MECHANIC. 

bounty of a good Providence, is not the condi- 
tion of mechanics here. They may — in fad 
they must neglect the cultivation of their 
minds ; but the American mechanic is inexcus- 
able if he neglects the great privileges which 
distinguish him from the less fortunate Euro- 
pean. 

Another reason why the American mechanic 
should cultivate his intellectual powers as far 
as possible, is the vastly wider field which is 
opened to him by the extent and the resources 
of his country, and the ever active enterprize 
of its citizens. The European mechanic is 
hedged in on every side by restriction, and by 
competitors without number. All the trades 
there are full. In our country we see the re- 
verse. Here we have not men enoi, ^h to per- 
form the work required. The demana for me- 
chanical industry has never been fully met, and 
cannot be, for a long time to come. The im- 
mense amount of our land, the preponderance 
of agricultural industry, and the increasing de- 
mands of commerce, open an unlimited field to 
mechanical enterprise. We may infer what 
may yet be done from what has already been 
done. The service which the mechanical in- 
genuity of Americans has already rendered to 



TRIUMPHS OF AMERICAN INGENUITY. £3^ 

ilie country is at once a source of pride and of 
hope. Take, for example, the service rendered 
to the cotton growing interest by Whitney's 
invention of the saw-gin ; or that rendered to 
internal commerce and to agriculture by Ful- 
ton's introduction of the steamboat into general 
use ; or that rendered to every consumer in the 
country by inventors and manufacturers con 
cerned in the production of cotton and woollen 
fabrics. These inventions and improveme 
by increasing the resources of the country, haye 
greatly increased the demand for mechanical 
products. Whether, therefore, the 'American 
mechanic addresses himself to increasing the 
quantity or improving the quality of his manu- 
factures, the field before him is wide enough 
for his greatest powers and his most unwearied 
activity, in entering upon this field, let him 
remember that knowledge is power, and he 
will neglect no opportunity of impr ing his 
mind. 



21 



240 



THE YOUNG MECHANIC 



CHAPTER VII. 

MEANS OF INTELLECTUAL CULTIVATION 
ACCESSIBLE TO THE MECHANIC. 



Supposing that the reasons why an American 
mechanic should be well educated are suffi- 
ciently established, let us next consider the 
means which are at his disposal or may be 
brought within his reach. 

1. Of course the first and most important 
means of intellectual cultivation are the schools ; 
and those to the improvement of which the 
efforts of mechanics as a body can be most 
serviceably directed are the public schools. 
Wherever a system of public schools exists, it 
is the interest of the mechanic, in common 
with all other citizens, to aid in rendering it as 
perfect as possible. I believe that it is essen- 
tial to the perfection of a system of public 
schools, that not only elementary instruction 
should be dispensed to the children of all citi- 
zens who require it; but that schools of a 
higher order should be placed within the reach 
of all pupils whose parents mav wish to obtair 



SCHOOLS. 24\ 

the advantages of higher instruction for their 
oilspring. Experience shows that it is not a 
difficult matter to create a supply of this highei 
instruction equal to the demand, even where 
the provision of primary instruction is most 
abundant. In Boston, where the population is 
over eighty thousand, and the primary and 
grammar schools are sufficient to accommodate 
every applicant for admission without delay, 
the Higli School for twenty years has averaged 
only ninety pupils ; this being the whole mim 
ber of qualified candidates offered for admis 
sion. 

In Philadelphia the supply has certainly been 
hitherto equal to the demand, as all applicants 
for admission to the High School who were 
qualified for the higher studies at the time of 
their examination have been admitted. I be 
lieve that the number of scholars who will 
•eave the school every year to enter upon the 
active business of life, will always be found 
equal to those who shall be qualified for admis- 
sion and shall present themselves for exami- 
nation. The advantages resulting from High 
Schools are not confined to the pupils who re- 
ceive instruction at those schools. The stimu- 
lus afTo-ded by the hope of attaining admission 



242 TIIE YOUNG MECHANIC. 

to them arts upon all the other schools, pro- 
ducing greater exertion and a more rapid pro- 
gress in learning. In fact the whole system is 
not only improved, but greatly extended, by 
the existence of higher classes of schools 
This is apparent in this city,* where a greater 
number of primary and grammar schools have 
been created since the erection of the High 
School than at any previous period of the same 
length. The High School furnishes to the 
future mechanic precisely the liberal kind of 
instruction which will be most available to him 
in his trade ; and in some instances gives mi- 
nute practical information directly applicable to 
the arts ; as for example, in the mathematical and 
drawing lossons, and the lessons, lectures and 
experiments on chemistry, natural philosophy 
and natural history ; other parts of the course of 
instruction, as the training in logic, rhetoric 
a<id composition, have more direct reference to 
the pupiPs future position in the community as a 
citizen, a public officer, a parent, or a teacher. 
Such institutions it is the interest of every man 
to sustain ; of the rich, who do not avail them- 
selves of this advantage for their own children, 

* Philadelphia. 



MECHANICS' INSTITUTES. 24^ 

equally with those who are not rich, and there- 
fore need their aid. In fact, the laws which dis- 
tribute property equally among heirs, render it 
probable that the grand-children, or great-grand- 
children of the richest man in any of our com* 
munities will become pupils in the public 
schools. It is, therefore, the rich man's in- 
terest to pay heavy taxes, if need be, in ordei 
that the public schools may be rendered perfect. 
2. The inheritance which he will thus trans- 
mit to his posterity, will last long after his 
wealth shall have been scattered to the winds 
I pass with reluctance from this interesting part 
of the subject, to the next means of intellec- 
tual improvement for the mechanic, viz. : the 
Mechanic's Institute. Any youth who has 
been taught to read and write, may derive ad- 
vantages from the lectures, experiments and 
library of the Mechanic's Institute; and the 
system of operations in these admirable insti- 
tutions is so liberally expanded, that the most 
accomplished scholar may also increase the 
amount of his practical knowledge by having 
recourse to the means of improvement which 
they allbrd. 3. But the best of all instruction 
is self instruction, and the most available means 
vh : "h the young man who is determined to 
21* 



244 TIIE YOUNG MECHANIC. 

instruct himself can employ, are the library am! 
the apparatus which are immediately at his own 
disposal — under his own roof — in his own apart- 
ment. The great secret of self improvement 
is to dedicate a portion of every day to private 
study. Consult the biographies of a long line 
of self taught men who have advanced science 
and the arts by their individual exertions, and 
you will find in most instances that the bril- 
liant discovery which astonished the world 
was the result of private study and unassisted 
experiment. You will find also that the houi 
redeemed from ordinary business, and conse- 
crated to some favourite scientific inquiry, was 
the great discoverer's choicest recreation, the 
delight of the day, the great reward of many 
labours and cares. We all have our favourite 
enjoyments, apart from our daily labour. While 
one man reads for recreation, another plays 
upon the flute or takes a ride, or sketches a 
landscape, or talks politics, or tells stories to 
his children. All these amusements are excel- 
lent and refreshing in their season — all are 
looked forward to with pleasure; but a sweeter 
recreation than any of these awaits the man 
who is at once a hard worker and a devotee of 
science. Often in the course o[ a busy day do 



MECHANICS' INSTITUTES. O45 

his thoughts bound forward to the happy mo- 
ment when he shall enter the sanctuary of his 
own study, leaving his toils and cares behind, 
md, " the world forgetting, by the world for- 
got," shall busy himself in his favourite pur- 
suits, studying, experimenting, calculating, till 
his brain is weary with pleasurable excitement, 
and tired nature claims the right of repose. In 
order to profit by study it is not absolutely ne- 
cessary, but it is certainly very convenient and 
agreeable to have a place, a room, be it ever so 
small or so poorly furnished, which the stu- 
dent, the self instructer, may call his own — his 
castle — his sanctuary. Here he treasures up 
his little library of books, few perhaps, but 
choice and well beloved. Here he has his 
desk, papers, and his collection of curious or 
useful things, each fraught with associations, 
each the occasion of a lesson to himself. The 
mineral, which is but a common pebble to the 
visitor who comes in to look at his cabinet, has a 
magic power in it for the collector himself. It 
brings back to his recollection the glorious 
mountain towering to the skies — the cataract — 
the deep cavern, or the broad prairie, where the 
wonderful gem was found — wonderful by the 
oower of association which it has over the mind 



246 



THE YOUNG MECHANIC. 



of its finder. The well worn volume, which is 
mere paper and print to another, is a precious 
treasure to him, who has learnt from it the great 
laws of nature, the lore of antiquity, or the 
sweets of poetry. Every article in this retreat 
of studious leisure has a value to the owner, as 
it is connected with the developement of his 
higher faculties. Every article is praised for 
having been, in its turn, the instrument of self 
cultivation. It would occupy too much time to 
enter here into a detailed review of the various 
means of self cultivation to which the student 
may have recourse in the retirement of his own 
room. These will form the subject of a future 
fliapter. 



INTELLECTUAL CULTIVATION. 24? 



CHAPTER VIII. 

REWARDS OF INTELLECTUAL CULTIVA- 
TION ACCESSIBLE TO THE MECHANIC. 

I will now offer a few remarks on the re- 
wards of intellectual cultivation. Liberal know- 
ledge, like virtue, is in a certain sense its own 
reward. The developement of the intellectual 
powers is attended with positive gratification, 
resulting from a sense of increased power, and 
the satisfying of curiosity respecting the laws 
of nature. The famous story of the rapture 
of Archimedes when he arrived at his beautiful 
demonstration of a well known mathematical 
truth, is but one among a thousand proofs that 
science rewards her votaries on the instant, 
pays her workmen, in solid coin, by the day — 
by the hour. This is the sweetest and best 
reward of intellectual labour. It is that which 
is most diligently sought and most highly 
prized. 

But there are other rewards, only incidental 
and inferior, but still worthy of some conside- 
ration. 



248 



THE YOUNO MECHANIC. 



1. Liberal knowledge and accomplishments 
confer the advantage of an elevated and influ- 
ential position in society. It is generally un- 
derstood that society exacts from each of its 
members some price of admission to its cote- 
ries and saloons. One brings fashion, another 
the wealth and consequence of his family, 
another his musical or conversational talents, 
another his celebrity as an author or traveller, 
or distinguished stranger. Among the rest the 
votary of science prefers his claim, and finding 
it admitted, takes a place in society on an inde- 
pendent and respectable ground. He is ad- 
mitted for what he is, not for what he has, or 
what his ancestors had. 

2. Again, liberal knowledge gives its posses^ 
sor the means of enjoyment in sickness, in 
retirement, and in eld age. He who has learnt 
to converse with the master spirits of other 
times, is never at a loss for society or amuse- 
ment. Give him a book and he is happy — or, 
failfng the book, his previous cultivation makes 
the communion of his own thoughts or the 
practice of composition a sufficient occupation 
to pass delightfully those hours of loneliness 
and silence which are a weariness to the illite- 
rate man. 



INTELLECTUAL CULTIVATION. 24& 

3. To the advantages which the scientific 
mechanic enjoys in the prosecution of his trade 
we have already adverted. We will name bin 
one more before closing the present considera- 
tion of the subject. It is this : — The members 
of any particular trade, by earnestly uniting in 
the use of the various means of intellectual 
cultivation within their reach, may greatly in- 
crease the respectability, wealth and influence 
of that trade. By possessing their own library, 
reading room, museum and apparatus, and by 
stimulating the exertions of every member of 
the trade, master, journeyman, and apprentice, 
they will soon come to be recognised as a 
scientific body ; and will not only insure to 
themselves the other rewards of science, but 
will receive the grateful acknowledgments of 
their fellow citizens as public benefactors. 

Such are the rewards of intellectual cultiva- 
tion attainable by those who are engaged in the 
mechanical trades. The example of Franklin, 
Watt, Ark wright, and a host of other iHustrious 
men, show what mechanics have done. It re- 
mains for the rising generation in our own 
happy land to show what mechanics can do. 



250 THE YOUNG MECHANIC 

CHAPTER IX 
THE MECHANIC'S STUDIES. 

Books are, generally speaking, too volumin- 
ous ; writers descend too much into minutiae : 
and it is an old observation, that where men 
are determined t"> write every thing which can 
be said on any subject, they may write to 
eternity. Hence it is that a man of sense and 
erudition need but open a single page of many 
a modern volume to lay it aside forever. It is 
said of Didymus, an ancient grammarian, that 
he had written so much that he knew not his 
own productions, and having once abused a 
work for its absurdity, it was found to be his 
owi. I fear the race of Didymus is not extinct.* 

To read all books on all subjects would re- 
quire an uninterrupted attention during the 
longest life, even of an antediluvian. To read 
only the most celebrated, written in a few lan- 
guages, is an employment sufficient lo fill up 
every hour of laborious application. For the 

* Northmore. 



CHOICE OF BOOKS. 25. 

Rake then of saving time, and of directing the 
judgment of the inexperienced, it becomes an 
useful attempt to suggest some general hints, 
which may tend to facilitate selection. One 
rule of the greatest consequence is, to read 
only, or chiefly, the original treatises in all the 
various departments of science or of literature. 
Nearly the same space of time, though not the 
same degree of attention, is necessary to peruse 
the faint copies of imitative industry, as would 
appropriate to the student the solid productions 
of native genius. This rule is more particu- 
larly to be observed on the first entrance on 
study. The foundation must be laid deeply, 
and formed of solid materials. The superstruc- 
ture will often admit slight and superficial ap- 
pendages. When we have studied the fine 
relics of those who have lived before us, we 
may derive much pleasure from attending to 
the additional labours of contemporary genius. 
But to begin with these is to found, like the 
fool recorded in the gospel, an edifice in the 
sand.* 

Tp* merit of a book consists in, 1, New 
facts ; 2. New inferences from established facts : 



* Knox's Essays. 
22 



252 THE YOUNG MECIIAN C. 

3. A better arrangement ; 4. A more complete 
collection of facts ; 5. Information. When a 
book is destitute of these requisites, it may be 
condemned, without mercy, as of no use what- 
ever, and immediately sold by weight to the 
cheesemonger, or consigned to any othei base 
or more ignoble purpose. When it is not des- 
titute of these, it should be reprieved, acquitted, 
or applauded, according to the requisites which 
it possesses.* 

On the choice of books, most excellent ad- 
vice is given by Dr. Watts, from whom, and 
other authors, has been compiled a pocket 
volume u on the Improvement of the Mind," 
in which various interesting matter relating to 
books, reading, conversation, study, 8cc. are 
treated of. Happy are they, says Fenelon, 
who being disgusted with all violent pleasures, 
know how to content themselves with the 
sweets of an innocent life. Happy are they, 
who are diverted, at the same time that they 
are instructed, and please themselves by en 
liching their minds with knowledge. Where- 
ever they may be thrown by adverse fortune, 
they will carry their own entertaii ment with 

• Dr. Moslev. 



CHOICE OF BOOKS. 253 

them; and the uneasiness, which preys on 
others, even in the midst of their pleasures, is 
unknown to those who can employ themselves 
in reading. Happy are they who love books 
and are not deprived of them. 

Among the other improvements of the pre- 
sent age, the art of puffing appears to have 
arrived at such perfection that it is impossible 
to select books by their titles, or from some of 
our booksellers' account of them in their ad- 
vertisements. A person who would make a 
preference and choose the best, must read much 
beyond the title page. From a hand bill which 
accidentally lies on the compiler's desk, the 
following encomiums are bestowed on very 
unmethodical and inferior works. " A fasci 
nating introduction, superior to every preceding 
attempt of the kind, and deserving of universal 
preference." " The most approved and gene- 
rally adopted book ever published, and un- 
doubtedly the best extant." Such parade of 
applause may pass with those who do not 
compare and discriminate, and their number is 
unfortunately not small. 

Mr. Pratt ingeniously laments the strange 
circumstance, that authors themselves have 
been the most bitter detractors of the talents 



254 THE YOUNG MECHAN/C. 

and reputations or each othei. A grievance 
far more disgraceful, if not more injurious, to 
the literary character, than any other species 
of criticism. Indeed it would be difficult to 
find any set of enemies among men, any per- 
sons, whose passions and interests are at va- 
riance, so full of acerbity, of open violence, or 
of concealed malice, as the most eminent writers 
have proved themselves to each other, in their 
contentions of rivalry. The " republic of let- 
ters" is a very common expression among Eu- 
ropeans, and yet, when applied to the learned 
of Europe, is the most absurd which can be 
imagined, since nothing is more unlike a repub- 
lic, than the society which goes by that name 
In truth, almost every member of this fancied 
commonwealth is desirous of governing, and 
none willing to obey : each looks upon his 
fellow as a rival, not an assistant in the same 
pursuit. They calumniate, they injure, they 
despise, they riuicule, they worry, and assas- 
sinate each other. If one man write a book 
which pleases, others write books to show that 
he might have given still greater pleasure, or 
should not have attempted to please. If one 
happen to hit upon something new, numbers 
are ready to assure the public that all this was 



CHOICE OF BOOK3. 255 

no novelty to them or the learned ; that Car- 
tlanus, or Brunus, or some other author, too 
dull to be generally read, had anticipated the 
discovery. Their jarring constitution, instead 
of being styled the republic of letters, should 
be entitled the anarchy of literature. It is true, 
there are some of superior abilities, who reve- 
rence and esteem each other ; but their mutual 
admiration is not sufficient to shield off the 
contempt of the crowd. The wise are but 
few, and they praise with a feeble voice ; the 
vulgar many, and roar in reproaches. The 
truly grrat seldom unite in societies, have few 
meetings, and no cabals : the dunces hunt in 
full cry, till they have run down a reputation, 
and then snarl and fight with each other about 
dividing the spoil." No task would be more 
easy to the most superficial observer, than that 
of producing numerous instances of glaring 
partiality in the journals of several of our cri- 
tics by profession. It appears sometimes from 
their neglect in reading with care the book 
which they undertake to criticize, so as to 
comprehend the author's views ; sometimes the 
narrowness of party spirit warps their decisions, 
m open contempt of the power of genius and 
originality. Sometimes a publisher's name on 
22* 



256 



THE YOUNG MECHANIC. 



the cover, connected with the imprint of the 
book, is a clue by which neglect, injustice, 
narrow-minded selfishness, and misrepresenta- 
tion, may be unravelled; and sometimes the 
critic's private jjique, as a contemporary author, 
is obvious. 

Poetic compositions, whether in ancient or 
modern languages, may be read at vacant hours, 
with some advantage, because many passages 
contain practical rules relating to moral econo- 
my and religion. Many elegant and ingenious 
sentiments and descriptions may also be found 
among the writings of poets, well worth com- 
mitting to memory ; and the measure of verse 
greatly assists recollection. 

The mere art of rhetoric never yet formed 
an English orator. It is one of those artificial 
assistances of genius, which genius wants not, 
and of which dullness can little avail itself. 
But as excellent books have been written on 
this subject, the general scholar will not fail 
to pay it some attention. Let him then read 
Cicero on the Orator, and Quintilian's Insti- 
tutes, and he need not trouble himself with 
those meagre treatises which give a hard name 
to natural modes of expression, and teach us 
Uiat, like FJudibras, we cannot open our mouthy 



ELOCUTION AND RHETORIC. 251 

but out there flies a trope.* So much of rheto- 
ric as teaches the art of speaking and writing 
with elegance and dignity, in order to instruct, 
persuade and please, is certainly most valuable 
Grammar teaches only propriety ; but rhetoric 
raises upon it purity and clearness of language, 
elegant thoughts, variety of expression, and 
lively figures. The duty of the orator is to 
stats interesting truths with such probability 
and evidence as may gain belief, and with such 
force and simplicity as may produce conviction. 
He must be able to demonstrate, to delight, and 
to work on the passions. 

Probably nothing has contributed more to 
generate apposite habits of mind than the early 
taste for reading. Books gratify and excite our 
curiosity in innumerable ways. They force us 
to reflect. They hurry us from point to point. 
They present direct ideas of various kinds, and 
they suggest indirect ones. In a well written 
book we are presented with the maturest re- 
flections, or the happiest flights, of a mind of 
uncommon excellence. It is impossible tl»a< 
we can be much accustomed to such compa 
nions, without attaining some resemblance o. 

* Dr. KnoA. 



258 THE YOUNG MECHANIC. 

them. He who revels in a well chosen library* 
has innumerable dishes, and all of admirable 
flavour. His taste is rendered so acute, as to 
distinguish the nicest shades of difference. His 
mind becomes ductile, susceptible to every im- 
pression, and gains new refinement from each. 
His varieties of thinking baffle calculation, and 
his powers, whether of reason or imagination, 
become eminently vigorous.* 

Exclusive of all regard to interest, and of 
preparation for the exercise of any art or pro- 
fession, says Dr. Knox, a taste for pleasing 
books is surely eligible, if it were only for the 
sake of enabling an ingenious man to pass his 
days innocently, calmly, and pleasurably. The 
pleasures of letters are certainly great to those 
who have been early devoted to them, and they 
are of all others the easiest to be obtained. 
For with respect to books we may say, " These 
are friends, no one of whom ever denies him- 
self to him who calls ; no one takes leave of 
his visitor till he has rendered him happier and 
more pleased with himself. The conversation 
of no one of these is dangerous, neither is the 
respect to be paid to him attended with expense 

• Godwin's Enquirer 



ON A TASTE FOR READING. ^5^ 

If on may take what you please from them. 
What happiness, what a glorious old age awaits 
him who is placed under the protection of such 
friends ! He will have those whom he may con- 
sult on the most important, and the most trifling 
matter, whose advice he may daily ask concern- 
ing himself; from whom he may hear the truth 
without insult, praise without adulation, and to 
whose similitude he may conform himself."* 

As soon as we have obtained, by reading, a 
competent knowledge of a book or particular 
subject, it will contribute greatly to animate us 
in proceeding still farther, if we talk of it either 
with our equals in attainments, or with the 
learned and experienced. In such conversation 
we venture to advance an opinion; our self- 
love renders us solicitous to maintain it, we 
seek the book as an auxiliary, we therefore 
read it with eager attention. In this manner 
an attachment to books and literary employ- 
ments is gradually formed, and what began in 
labour or necessity, becomes a choice, and con- 
stitutes the most agreeable pleasure. 

There is no study so dry, but by fixing oui 
attention upon it, we may at last find it capa* 

* Seneca. 



2(30 THE YOUNG MECHANIC 

ble of affording great delight. Metaphysics 
and mathematics, even in their abstrusest parts 
are known to give the attentive student a very 
exalted satisfaction. Those parts, then, of hu- 
man learning, which in their nature are more 
entertaining, cannot fail of being beloved in a 
high degree, when the mind is closely and con- 
stantly applied to them. 

In order to acquire the power and habit of 
fixing the attention, it will be first necessary to 
summon a very considerable degree of resolu- 
tion. In beginning the study of a new language, 
or any book of science, which presents ideas 
totally strange, the mind cannot but feel some 
degree of reluctance or disgust. But let the 
student persevere; and in a very short time 
the disgust will vanish, and he will be reward- 
ed with entertainment. Till this takes place, 
let him make it an inviolable rule, however 
disagreeable, to read a certain quantity, or for a 
certain time, and he will infallibly find, that 
what he entered upon as a task, he will conti- 
nue as his best amusement. 

A due degree of variety will contribute great- 
ly to render reading agreeable. For though 
it be true that not more than one or two books 
should be read at once; yet, when finished, it 



ON A TASTE FOR READING. OQ j 

will be proper, if any weariness be felt, to take 
up an author who writes in a different style, or 
on a different subject ; to change from poetry 
to prose, and from prose to poetry ; to inter- 
mix the moderns with the ancients ; alternately 
to lay down the book and take up the pen ; and 
sometimes to lay them both down, and enter 
with alacrity into agreeable company and pub 
lie diversions. The mind, after a little cessa- 
tion, returns to books with all the voracious 
eagerness of a literary hunger. But the inter- 
missions must not be long, or frequent enough 
to form a habit of idleness or dissipation. 

The morning has been universally approved 
as the best time for study ; but at all hours and 
in all seasons, if we can restrain the licentious 
rovings of imagination; soothe the passion 
of the heart, and command our attention, so as 
to concentre it on the subject we examine, we 
shall find it amply rewarded. Attend closely; 
and close attention to any worthy subject will 
always prove solid satisfaction. But particu- 
larly in reading it may be depended on as ap- 
proved truth, that the degree of profit as well 
as pleasure, derived from it, will ever be pro- 
portioned to the degree of attention.* 

* Knn's Essays, No. 82. 



262 THE YOUNG MECHANIC. 

There are some mechanic aids in leading, 
which may prove of great utility. Montaigne 
placed at the end of the book which he intend- 
ed not to reperuse, the time he had read it, 
with a concise decision on its merits. He has 
obliged hie admirers with giving several of these 
annotations. The striking passages in a book 
may be noted on a blank leaf, and the pages 
referred to with a word of criticism. Seneca, 
in sending some volumes to his friend Lucilius, 
accompanied them with notes on particular 
passages, that, as he observes, you who only 
aim at the useful, may be spared the trouble of 
examining them entirely. I have seen books 
noted by Voltaire with a word of censure or 
approbation on the page itself, which was his 
usual practice ; and these volumes are precious 
to every man of taste.* 

I would have every one try to form an 
opinion of an author himself, though mo- 
desty may restrain him from mentioning it. 
Many are so anxious to have the reputation of 
taste, that they only praise the authors whose 
merit is indisputable. 1 am weary of hearing 
of the sublimity of Milton, the elegance and 

* D'lsraeli's Miscellanies. 



ON A TASTE FOR READING. 26ri 

harmony of Tope, and of the original, untaugh. 
genius of Shakspeare. Such hackneyed re 
marks are made by those who know nothing 
of nature, and can neither enter into the spirit 
of those authors, nor understand them * 

Temperance in eating and drinking, will con- 
tribute more to improve the natural force or 
abilities of the mind, than any art or any ap- 
plication. It is related of the unfortunate young 
Chatterton, that he was remarkably abstemious, 
and that it was a frequent and favourite maxim 
with him, that a man might arrive at any height 
of improvpment, or effect the most arduous un- 
dertaking, by dint of industry and abstinence. 
lie practised what he thought; and this in some 
degree accounts for his uncommon attainments 
and productions, at an age when the full-fed 
heir can scarcely read and write. I recommend 
to all students the perusal of Dr. Cheney's 
Medical Advice; or I will give it to them in a 
few words. "Take the least and the lightest 
food, under which you can be easy." Your 
so*d will thus feel fresh vigour, your life will 
be longer and happier, and your conduct wiser.f 
The neglect of writing in early life is the 



Mai j Wotlstonecraft, fDr. Knox. 

23 



264 



THE YOUNG ME( HANIC. 



reason that almost every line of our scholars 
and gentry (who seem to pride themselves in 
their bad penmanship) stands in need of an in- 
terpreter. As this art is purely mechanical, and 
perfected by practice only, it is foreign from 
my purpose to prescribe rules for its attain 
ment. I will venture however to assert, that a 
plain, upright hand, resembling the round ro- 
man print is preferable to the ridiculous flour- 
ishes and slopes of writing-masters ; and my 
opinion is founded on a very simple reason, i f 
is more legible* 

Plain writing, says Dr. Gregory, clear of 
flourishes, and very upright, is certainly the 
most proper for every station of life, and will 
remain intelligible longer than any other. It 
may be learned with less time and trouble, and 
may be written more expeditiously. 1 have 
long been of this opinion, and was happy to 
find it countenanced by the authority of Dr. 
Knox, and Dr. Beattie. Their popularity may 
perhaps be of weight in correcting the whimsi- 
cal and unintelligible mode of writing, which 
has been introduced by ignorant schoolmasters 
\ perfectly agree with the latter, that the writing 

* Yorke. 



ON THE ART OF WRITING. 265 

which approaches nearest the Roman printea 
character, is the completest. Pope was taught 
to write by imitating and copying the Roman 
character of printed books, in which kind of 
writing b<? always excelled. [The Italic printed 
character appears better adapted for the purpose 
of writing than the Roman.] A gentleman in- 
formed, by letter, his country friend in Lin- 
colnshire, who had done him some recent fa- 
vour, how much he was obliged, and that he 
should soon send him an equivalent. Not being 
accustomed to fashionable scrawls, he read it 
that his friend would send him an elephant , 
and, building a barn at the time, actually fitted 
up a stall for the reception of his expected pre- 
sent. The arrival, however, of a barrel of 
oysters, a few days afterwards, helped him to 
the right reading, by putting him in possession 
of a more suitable equivalent than an elephant, 
This is a fact, and occurred a few years since.* 

•Rede's Anecdotes, 1793. 



20(5 THE YOUNG MECHANIC 

CHAPTER X. 

THE MECHANIC'S STUDIES. 

To learn the rudiments of grammar by rote, 
is not the way to understand grammar. The 
mind must be addressed and convinced. Of 
what use is it to vex a boy's memory with the 
definition of a noun, when the definition itself 
is not clear to his understanding ? We may as 
well show him the figure of a triangle on pa- 
per, and expect him to comprehend its nature, 
by a definition of its properties. The fact is, 
the tender mind is not capable of abstract rea- 
soning; consequently, every subject which im- 
plies the generalization of ideas, should be first 
unfolded by evident and palpable demonstra- 
tion. Thus, a boy is taught in our schools to 
gabble that " a noun is the name of any per- 
son, place, or thing, as John, London, Honour ;" 
yet I will venture to assert, that not one in ten 
thousand comprehends what he says. An 
analysis of language was never formed, until 
men were enabled to observe the turns of 
speech which custom authorizes ; there were 



ON LEARNING A LANGUAGE. 26V 

poets and orators before a grammar was evei 
thought of; it would be useless to teach eithei 
systems of rhetoric or composition to a child, 
who had not learnt, by frequent use, the proper 
idioms of his own language ; and that there- 
fore the best models of beautiful writing should 
be set before him, previous to his being brought 
to judge of them by any determined rules.* 

If grammar be taught, it must be to one who 
can speak the language ; how else can he be 
taught the grammar of it ? This is evident 
from the practice of the wise and learned na- 
tions among the ancients. They made it a part 
of education to cultivate their own, not foreign 
tongues. The Greeks counted all other nations 
barbarous, and had a contempt for their lan- 
guages. And though the Greek learning grew 
in credit among the Romans, towards the end 
of their commonwealth, yet it was the Roman 
tongue which was made the study of their 
youth. It was their own language which they 
were to make use of, and therefore it was their 
own language they were instructed and exer- 
rised in. 

Rut more particularly to determine the pio- 



*H R Yorke. 
23* 



26S THE YOUNG MECHANIC. 

per season for grammar, I do not see how it 
can reasonably be made any one's study, but 
as an introduction to rhetoric. When it is 
thought time to put any one on the care of 
polishing his. tongue, and of speaking bettei 
than the illiterate, then is the time for him to 
be instructed in the rules of grammar, and not 
before : for grammar is designed not only tc 
teach men to speak, but to speak correctly, and 
according to the exact rules of the tongue, 
which is one part of elegancy ; there is little 
use of the one to him who has no need of the 
other ; where rhetoric is not necessary, gram- 
mar may be spared.* 

The cumbersome heap of worthless rules 
with which grammars are crowded, has urged 
some into the extreme of discarding them, 
They have observed that a quicker progress 
has been made in a language by learning it by 
mere rote, and from thence have extravagantly 
concluded that grammars are unnecessary. 
Without the assistance of the rules of con- 
struction, it is difficult to speak the living lan- 
guages well ; to say nothing of reducing sci- 
ence to principles, which contribute to form 

* Locke. 



ON LEARNING A LANGUAGE. 269 

the judgment. But grammars ought to be con- 
structed rationally, whereas many, so far from 
being adapted to the capacities of children, sup- 
pose them to be half philosophers in the outset. 
This is evident from the connection which the 
rules have with things with which children are 
unacquainted.* 

With a view of making the study of language 
agreeable and pleasant, particularly to boys, it 
is necessary that the subject on which students 
are employed to read, be interesting. The 
judicious teacher can easily collect authors, in 
almost every language, whose writings are cal- 
culated to arrest and interest the mind at an 
early period of life. In order, however, to 
render the study and comprehension of such 
works easy, difficult passages should always be 
satisfactorily explained in the student's vernacu- 
lar tongue, by notes ; and they should, for be- 
ginners, be accompanied with literal transla- 
tions.! 

Two things are requisite in learning a lan- 
guage ; a knowledge of words, and skill in 
putting them together in writing or speaking. 
The foimer is much the more easy of the two, 

* De 1'Education par M. de Crousaz. f Dr. Cowan 



270 THfi YOUNG MECHANIC 

and consequently ought to go first : to intermix 
any foreign stuff, as grammar with it, is throw 
ing an obstacle in the way of boys, and hin- 
dering their progress. They are to be kept to 
but one thing at a time, as much as possible 
To trouble them with variety, unless by way 
of refreshing their memories, or to prevent their 
forgetting what they have already learnt, I think 
a grand mistake in education, and one main 
occasion of that miserable work which boys 
make of it in most schools. 

Though grammar be a matter of importance, 
the parts of language which relate to the signi- 
fication of words, and phraseology are of 
greater importance. In the latter departments, 
a pupil cannot be overburdened •, in the former, 
there are many things not worth committing to 
memory ; and he who intends to make a boy a 
critic in grammar, will unavoidably leave him 
deficient in other more necessary things. It 
would be the same as if a man should take 
care to let his son be furnished with elegant 
shoes, while the rest of his body was clothed 
in rags.* 

I very much doubt whether any child, pro 

* Clarke's Essay on Education. 



ON LEARNING A LANGUAGE. 07^ 

dixies excepted, be capable of learning two 
languages, till it arrive at the age of twelve or 
thirteen, 1 have indeed seen little wonderful 
prattlers, who were imagined to talk five or six 
different languages. I have heard them suc- 
cessively talk in German, in Latin, French, and 
Italian words. They made use, it is true, of 
the different terms of five or six dictionaries; 
but they spoke nothing but German. In a word, 
fill a child's head with as many synonymous 
terms as you please, you will change his words 
only, but not his language, for he can know 
but one. No sooner have they gone through 
the rudiments of the grammar, of which they 
absolutely understand nothing, than they are 
set to render a discourse spoken in their native 
tongue into Latin words ; when they are ad- 
vanced a little farther, they are engaged to patch 
up a theme in prose, by tacking together the 
phrases of Cicero, and in verse with centos from 
Virgil. They then begin to think themselves 
capable of talking Latin. And who is there to 
contradict them.* 

To learn a language grammatically, or even 
to speak it, allowing for bad pronunciation, is 

* Rousseau, h. 2. 



272 THE VOUNG MECHANIC. 

at any time of life an easy acquisition. Wc are 
told that Themistocles learnt the Persian lan- 
guage in one year, and a year is sufficient time 
to learn any language. It is too great an atten- 
tion to the rules of grammar which retards our 
improvement. Rousseau has therefore properly 
warned us against correcting the grammatical 
errors of children, who never fail in due time 
to correct themselves. Mr. Locke recommends 
the same method to be adopted in learning the 
dead languages. u The Latin tongue," he ob- 
serves, " would easily be taught, if the tutor 
being constantly with his pupil would talk 
nothing else to him, and make him answer still 
in the same language." But to this reasoning \ 
object ; for, not to mention the difficulty of find- 
ing tutors who can speak these languages well, 
it is the constant daily habit of conversing with 
every one around us, which facilitates the ac- 
quisition of living tongues, and this is particu- 
larly the case with children, who learn more in 
one hour's game of play with their equals, than 
in a day's discourse with their tutors. Another 
strong objection to this method arises from its 
inutility. The only use of learning the dead 
languages is, as Milton says, to " study the 
solid things in them." Now even allowing 



ON LEARNING A LANGUAGE. 273 

that a pupil may be competent to hold a con- 
versation in Latin, which certainly is making a 
great allowance, if we take into consideration 
the difficulty of applying an ancient language 
to modern customs, yet he will reap but little 
benefit from this acquisition when he comes 
to read the philosophic works of Cicero, or 
Quintilian, or the histories of Livy or Tacitus. 
The same reasoning is in some measure appli- 
cable to modern tongues. A foreigner who can 
speak English well, may be unable to compre- 
hend either the sublime beauties of Shakspeare, 
or the nervous eloquence of Johnson. But 
though I dissent from Mr. Locke as to the best 
means of acquiring the dead languages, yet of 
the method which I am now about to propose, 
I speak with the greater confidence, being sup- 
ported in my opinion not only by my own ex- 
perience, but by the practice of Roger Ascham, 
the celebrated tutor to Queen Elizabeth. The 
custom established in schools of obliging the 
scholars to learn the grammar by heart, cannc t 
be too much deprecated. The grammar, like 
the dictionary, is only a book of reference ; u io 
read it therefore by itself, is," as Ascham well 
observes, " tedious for the master, hard for the 
scholar, cold and uncomfortable for them both." 



274 THE VOUNG MECHANIC. 

It certainly is irksome for boys who have it to 
learn, because it conveys no pleasurable ideas, 
and much time is thus unnecessarily lost. Mr. 
Dyer in his life of Robinson, has observed that 
iC Mr. Robinson's way of acquiring a knowledge 
of languages, was to sit down to an author, 
without any previous knowledge of the gram- 
mar, and to refer only to it in the same manner 
as the dictionary." This being premised, let 
us now suppose that my pupil is to be instruct- 
ed in the Greek language. He accordingly 
procures a grammar and dictionary ; but instead 
of labouring a twelvemonth in committing the 
former to memory, he reads it over once or 
twice merely to acquire some little insight into 
the nature of the language. His tutor then 
procures for him the best work of the purest 
Greek writer; suppose the Republic of Plato, 
or the Cyropaedia of Xenophon, which is bet- 
ter adapted to youth. We now sit down to- 
gether, with our pens, ink and paper, to translate 
one of the easiest passages, making due refer- 
ence to our grammar and dictionary. Having 
done this we shut our books, and put our 
translations carefully by in our drawers. We 
then proceed to other business ; perhaps to the 
carpenter's chest, or the garden tools. The 



ON LEARNING A LANGUAGE. o?5 

next morning we take out our translations, and 
retranslate them into the best Greek we are 
able, which we compare with, and correct by 
the original text. This translation and retains- 
lation, increasing gradually in quantity, we con- 
tinue to practise, till we become masters of the 
language, never omitting a single day, how 
small soever be the portion. It should be re 
membered, that, as we increase in knowledge, 
the version of one day is not retranslated till 
the interval of three or four days has elapsed, 
in order that the pupil may not translate by 
rote. By these means the language is learnt 
not only with greater facility, but to much 
greater perfection ; for the scholar acquires a 
knowledge of the peculiar cast of the language, 
and the particular points in which it differs 
from his own. Another advantage attending 
this system of translation, is, that the pupil 
cannot suffer from the ignorance of his tutor, 
both of them having the best possible standard 
for their guide. Nor perhaps is it a matter of 
small importance that the tutor is improving 
I imself, at the very time that he is instructing 
his pupil ; and I am certain that the appearance 
only of studying one's-self, tends much to in- 
crease the love of study in youth. 



276 THE *OUNG MECHANIC. 

In addition to translating, we must not omit 
to mention the advantages which accrue, par- 
ticularly to maturer minds, from reading and 
reciting the works of the great masters. By 
this we imbibe not only a taste for their purity 
and elegance of diction, but frequently partici- 
pate of their animation, and the fire of their 
genius.* 

Let none despair of acquiring, not only a 
competent but a critical knowledge of language, 
at whatever age a taste for such studies may be 
imbibed. Julius Scaliger, a profound critic, 
knew not the letters of the Greek alphabet at 
the age of forty years. Dr. Franklin learnt to 
speak French when upwards of seventy. Eu- 
gene Aram, without any assistance, learnt Latin, 
Greek, Hebrew, French, Chaldee, Arabic, and 
the Celtic. 

Whatever be the advantages, or defects of 
the English language, as it is our own language, 
it deserves a high degree of our study and at- 
tention, both with regard to the choice of word* 
which we employ, and with regard to the syntax 
oi' the arrangement of these words in a sentence 
V\e know how mnch the Greeks and the Ro- 

* I^o.tiwio.e. 



THE ENGLISH LANGUAGE. 



27> 



mans, in their moat polished and flourishing 
times, cultivated their own tongues. We know 
how much study both the French and the Ita- 
lians have bestowed on theirs. Whatever know- 
ledge may be acquired by the study of other 
languages, it can never be communicated with 
advantage, unless by such as can write and 
speak their own language well. Let the matter 
of an author be ever so good and useful, his 
compositions will always suffer in the public 
esteem, if his expression be deficient in purity 
and propriety. At the same time, the attain- 
ment of a correct and elegant style, is an ob- 
ject which demands application and labour. If 
any imagine they can catch it merely by the 
ear, or acquire it by a slight perusal of some 
of our good authors, they will find themselves 
much disappointed. The many errors, even in 
point of grammar, the many offences against 
purity of language, which are committed by 
writers who are far from being contemptible, 
demonstrate, that a careful study of the lan- 
guage is previously requisite, in all who aim 
tt writing it properly.* 
The application of a child to a dead Ian- 



*Dr Blair. 



278 



THE YOUNG MECHANIC. 



guage, before he be acquainted with his own, 
is a lamentable waste of time, and highly de- 
trimental to the improvement of his mind. The 
general principles of grammar are common to 
all languages ; a noun is the same in English, 
French, Latin, Greek, &c. The varieties of 
languages are easily acquired by observation 
and practice, when a preliminary knowledge of 
our own grammar is obtained, But, the com- 
prehension of our native tongue, is not t\it 
only good preparative for the study of other 
languages. Some previous acqaintance with 
the general nature of things is necessary to the 
accomplishment of this end, in order that our 
literary progress may not be obstructed merely 
by words. For, although it be useful to leave 
some, difficulties in the way of a child, that he 
may exercise his mind in overcoming them, yet 
he must not be disgusted by too many or too 
great impediments. Our whole attention should 
consist in proportioning the difficulties to his 
powers, and in offering them to his considera- 
tion individually. If Latin were made the pri 
mary object of a child's lesson, he would lose 
a vast portion of time in the study of grammar ; 
he would be incapable of perceiving the beau- 
ties of that language, because he would 1101 



THE ENGLISH LANGUAGE. 27^ 

frtve acquired any previous knowledge. ~No 
benefit therefore could possibly accrue, from 
reading in the Latin tongue subjects which he 
could not understand in his own. But, by his 
becoming well acquainted with our best poets 
and prose writers, he will easily learn, inde- 
pendently • of the number of ideas which he 
will gain thereby, the general rules of gram- 
mar : several examples will unfold them, and a 
proper application of others may be soon made 
without difficulty. Besides, he will acquire 
taste and judgment, and be well prepared to 
feel the beauties of a foreign tongue, when he 
begins to feel the beauties of his own. His 
knowledge being also extended and diversified, 
it will be found that the sole difficulty attendant 
on the study of Latin, consists in learning 
words ; so that to obtain a just knowledge of 
things he must apply himself to such Latin 
authors only as are within the reach of his 
capacity, and whose writings he can compre- 
hend with the same facility as if they were 
written in his native language. By this plan, 
he will easily acquire the Latin tcngue, trea- 
sure up fresh knowledge as he advances, and 
jxperience no disgusts in the study of it. 
Nothing can be more useless than to fatigue a 
24* 



9§0 THE YOUNG MECHANIC 

child, by filling his memory with the rules of 
a language which he does not yet understand. 
For. of what advantage is the knowledge of ita 
rules, if he be unable to apply them ? We 
should wait, therefore, until reading has gradu- 
ally enlightened his mind, and the task becomes 
not irksome to him. When he has studied his 
own language, we should anticipate the princi- 
pal difference between the Latin and English 
syntax. His surprise in perceiving an unex- 
pected difference, will excite his curiosity, and 
effectually remove all distaste. After this, and 
not before, we may devote a part of each day 
to Latin ; but it ought never to be the first ob- 
ject of his studies.* The best English Gram 
mar for the purpose of self instruction is Frost's 
Practical Grammar, published by Thomas, 
Cowperthwait & Co., Philadelphia. 

The Latin authors are possessed of uncom- 
mon excellence. One kind of excellence they 
possess which is not found in an equal degree 
;n the writers of any other country : an exqui- 
site skill in the use of language ; a happy se- 
lection of words ; a beautiful structure of 
phrase ; a transparency of style ; a precision 

• H. R. Yorke. 



THE LATIN LANGUAGE. gg] 

by which they communicate the strongest sen- 
timents in the directest form ; in a word, every 
thing which relates to the most admirable 
polish of manner. Other writers have taken 
more licentious nights, and produced greater 
astonishment in their readers. Other writers 
have, ventured more fearlessly into unexplored 
-egions, and cropped those beauties which hang 
over the brink of the precipice of deformity. 
But it is the appropriate praise of the best Ro- 
man authors, that they scarcely present us with 
one idle and excrescent clause, that they con 
tinually convey their meaning in the choicest 
words. Their lines dwell upon our memory ; 
their sentences have the force of maxims, every 
part vigorous, and seldom any thing which can 
be changed but for the worse. We wander in 
a scene where every thing is luxuriant, yet 
every thing vivid, graceful and correct. 

It is commonly said, that you may read the 
works of foreign authors in translations. But 
the excellencies above enumerated are incapa- 
ble of being transfused. A diffuse and volumi- 
nous author, whose merit consists chiefly in 
his thoughts, and little in the manner of attiring 
them, may be translated. But who can trans- 
late Horace ? who endure to read the trans la- 



282 THE YOUNG MECHANIC. 

tion ? 1 et who is there, acquainted with him 
only through this medium, but listens with 
astonishment and incredulity to the encomiums 
he has received from the hour his poems were 
produced ? The Roman historians are the best 
which ever existed. The dramatic merit and 
the eloquence of Livy ; the profound philoso- 
phy of Sallust ; the rich and solemn pencil of 
Tacitus, all ages of the world will admire. 
Add to this, that the best ages of Rome afford 
the purest models 'of virtue which are any 
where to be met with. Mankind are too much 
inclined to lose sight of all which is heroic, 
magnanimous and public spirited. Modern 
ages have formed to themselves virtue, rather 
oolished than sublime, which consists in petty 
courtesies, rather than in the tranquil grandeur 
of an elevated mind. It is by turning to Fabri- 
cius, and men like Fabricius,that we are brought 
to recollect what human nature is. Left to 
ourselves, we are apt to sink into effeminacy 
and apathy. It is by comparison only that we 
can enter into the philosophy of language. It 
is by comparison only that we can separate 
ideas, and the words by which those ideas are 
ordinarily conveyed. It is by collating one 
language with another that we detect all the 



THE LATIN LANGUAGE. 



28: 



shades of meaning through the various inflec- 
tions of sense which the same word suffers, as 
it shall happen to be connected with different 
topics. 

He who is acquainted witli only one Ian 
guage, will probably always remain in some 
degree the slave of language. From the im- 
perfectness of his knowledge, he will feel him- 
self at one time seduced to say what he did 
not mean, and at another time will fall into 
errors of this sort without being aware of it. 
It is impossible he should understand the full 
force of words. He will sometimes produce 
ridicule where he intended to produce passion. 
He will search in vain for the hidden treasures 
of his native tongue. He will never be able to 
smploy it in the most advantageous manner. 
He cannot be well acquainted with its strength ; 
and weakness. He is uninformed respecting 
its true genius and discriminating characteris- 
tics. But the man who is competent to, and 
exercised in the comparison of languages, has 
attained to his proper elevation. Language is 
not his master, but he is the master of language. 
Things hold their just order in his mind ; ideas, 
first, and then words. Words therefore are 
used by him as the means of communicating 



284 THE YOUNG MECHANIC. 

or giving permanence to his sentiments ; and 
the whole magazine of his native tongue is sub- 
jected at his feet. 

Latin is a language which will furnisli us 
with the etymology of many of our own 
words ; but it has perhaps peculiar recommen- 
dations as a praxis in the habits of investiga- 
tion and analysis. Its words undergo an un- 
common number of variations and inflexions. 
These inflections are more philosophically ap- 
propriated, and more distinct in their meaning, 
than the inflections of any language of a more 
ancient date. As the words in Latin composi- 
tion are not arranged in a philosophical or na- 
tural order, the mind is obliged to exert itself 
to disentangle the chaos, and is compelled to 
yield an unintermitted attention to the inflec- 
tions. It is therefore probable that the philoso- 
phy of language is best acquired by studying 
this language. Practice is superior to theory ; 
and this science will perhaps be more success- 
fully learned, and more deeply imprinted, by 
the perusal of Virgil and Horace, than by read 
ing a thousand treatises on universal grammar. 
Examples seem to correspond to what is here 
stated. Few men have written English with 
force and propriety, who have been wholly 



THE LATIN LANGUAGE. 



285 



unacquainted with the learned languages Our 
finest writers and speakers have been men who 
amused themselves during the whole of their 
lives with the perusal of the classics. Nothing 
is generally more easy than to discover by his 
style whether a man has been deprived of the 
advantages of a literary education. He who 
has not been accustomed to refine on words, 
and discriminate their shades of meaning, will 
think and reason after a very inaccurate and 
slovenly manner. 

Two qualities are especially necessarv *o 
any considerable improvement of humai* un- 
derstanding ; an ardent temper, and a habit of 
thinking with precision and order. The study 
of the Latin language is particularly conducive 
to the production of the last of these qualities. 
In this respect the study of Latin and geometry 
might perhaps be recommended for a similar 
reason. In the study of language and its in- 
flections, all is in order. Every thing is sub- 
jected to the most inflexible laws. The mind 
therefore which is accustomed to it, acquires 
habits of order, and of regarding things in a 
state of clearness, discrimination, and arrange- 
ment. 

The discipline of mind, here described, is 



2S6 THE YOUNG MECHANIC 

of inestimable value. He who is not initiated 
in the practice of close investigation is con- 
stantly exposed to the danger of being deceived. 
His opinions have no standard, but are entirely 
at the mercy of his age, his country, the books 
he chances to read, or the company he happens 
to frequent. His mind is a wilderness. It may 
contain excellent materials, but they are of no 
use. He is unable to regulate his mind, and 
sails at the mercy of every breath of accident 
or caprice. Such a person is ordinarily found 
incapable of application or perseverance. All 
talent may perhaps be affirmed to consist o( 
analysis and dissection, the turning a thing on 
all sides, and examining it in all its variety oi 
views. An ordinary man sees an object just as 
it happens to be presented to him, and sees no 
more. But a man of genius takes it to pieces, 
inquires into its cause and effects, remarks its 
internal structure, and considers what would 
have been the result, if its members had been 
combined in a different way, or subjected to 
different influences. The man of genius gains 
whole magazine of thoughts, where the ordi 
nary man has received one idea ; and hit 
powers are multiplied in proportion to the 
number of ideas on which they are to be era- 



THE LATIN LANGUAGE. O57 

ployed. Now there is perhaps nothing whici 
contributes more eminently to this subtilizing 
and multiplication of mind, than an attention 
to the structure of language. 

Let it be taken for granted that the above ar- 
guments sufficiently establish the utility o^ 
classical learning ; it remains to be determined 
whether it be necessary that it should form a 
part of the education of youth. It may be 
alleged, that, if it be a desirable acquisition, it 
may with more propriety be made when a per- 
son is arrived at years of discretion; that it will 
then be made with less expense of labour and 
time, that the period of youth ought not to be 
burdened with so vexatious a task, and that our 
early years may be more advantageously spent 
in acquiring the knowledge of things, than of 
words. In answer to these objections it may 
be remarked, that it is not certain that, if 
the acquisition of the rudiments of classical 
learning be deferred to our riper years, it will 
ever be made. It will require strong inclina- 
tion and considerable leisure. A few active and 
determined, spirits will surmount the difficulty ; 
but many who w r ould derive great benefit from 
the acquisition, will certainly never arrive at it. 
The age of youth seems particularly adapted 
25 



2S8 1IIE YOUNG MECHANIC 

to the learning of words. The judgment is 
then small, but the memory is retentive. In our 
riper years we remember passions, facts, and 
arguments ; but it is for the most part in youth 
that we retain the very words in which they 
are conveyed. Youth easily contents itself 
with this employment, especially where it is 
not enforced with particular severity. Acquisi- 
tions which are disgustful in riper years, art 
often found to afford young persons no con 
Cemptible amusement. It is not perhaps true 
that, in teaching languages to youth, we are 
:mposing on them an unnecessary burden. U 
we would produce right habits in the mind, it 
must be employed. Our early years must not 
be spent in lethargic indolence. An active ma- 
turity must be preceded by a busy childhood. 

It has often been said that classical learning 
is an excellent accomplishment in men devoted 
to letters, but that it is ridiculous, in parents 
whose children are destined to more ordinary 
occupations, to desire to give them a superficial 
acquaintance with Latin, which in the sequel 
will infallibly fall into neglect. A conclusion 
opposite to this is dictated by the preceding 
reflections. We can never foresee the fuftore 
destination, and propensities of our children; 



THE LATIN LANGUAGE g8S> 

yet, no portion of classical instruction, however 
small, need be wholly lost. Some refinement 
of mind, some clearness of thinking, will al- 
most certainly result from grammatical studies. 
Though the language itself should ever after 
bo neglected, some portion of a general science 
has thus been acquired, which can scarcely be 
forgotten. Though our children should be 
destined to the humblest occupation, that does 
not seem to be a sufficient reason for our de- 
nying them the acquisition of some of the most 
fundamental documents of human understand- 
ing.* 

The following method of teaching Latin, re- 
commended by R. L. Edgeworth, F. R. S., ap- 
pears exceedingly simple, natural, and pleasing, 
and furnishes useful hints for those who desire 
to teach themselves. " When children have by 
gentle degrees, and by short and clear conver- 
sations, been initiated in general grammar, and 
familiarized to its technical terms, the first page 
of tremulous Lilly will lose much of its horror. 
It is taken for granted, that the pupil can read 
and understand English, and that he has been 
eccustomed to employ a dictionary. He may 

* Godwin's Enquirer. 



290 T IIE YOUNG MECHANIC. 

now proceed to translate from some easy book. 
a few short sentences : the first word will pro- 
bably be an adverb or conjunction ; either of 
them may be readily found in the Latin dic- 
tionary, and the young scholar will exult in 
having translated one word of Latin ; but the 
next word, a substantive or verb, perhaps will 
elude his search. Now the grammar may be 
produced, and something of the various termi- 
nations of a noun may be explained. If musam 
be searched for in the dictionary, it cannot be 
found, but musa catches the eye, and with the 
assistance of the grammar it may be shown, 
that the meaning of words may be discovered 
by the united helps of the dictionary and gram- 
mar. After some days' patient continuation of 
this exercise, the use of the grammar, and of 
its uncouth collection of words and syllables, 
will be apparent to the pupil ; he will perceive 
that the grammar is a sort of appendix to the 
dictionary. The grammatical formula? may 
then, by gentle degrees, be committed to me- 
mory ; and when once got by heart, they should 
be assiduously preserved in the recollection 
After the preparation which we have recom 
mended, the singular number of a declension 
will be learnt in a few minutes, by a child ol 



TriE LATIN LANGUAGE. 29 \ 

oidinary capacity, and after two or three days' 
repetition, the plural number may be added. 
The whole of the first declension shoald be 
well fixed in the memory before a second be 
attempted. During this process a few words 
at every lesson may be translated from Latin to 
English, and such nouns as are of the first de- 
clension may be compared with musa, and may 
be declined according to the same form. Te- 
dious as this method may appear, it will in the 
end be found expeditious. Omitting some of 
the theoretic or didactic part of the grammar, 
which should only be read, and which may be 
explained with care and patience, the whole 
of the declensions, pronouns, conjugations, the 
list of prepositions, conjunctions, interjections, 
some adverbs, the concords, the common rules 
of syntax, may be comprised with sufficient 
repetitions in about two or three hundred les- 
sons of ten minutes each : that is to say, ten 
minutes' application of the scholar in the pre- 
sence of the teacher. A young boy should 
never be set to learn a lesson by heart when 
alone. Forty hours ! Is this tedious ? If you 
are afraid of losing time, begin a few months 
earlier ; but begin when you will, forty hours 
« surely no great waste of time ; th* whole, or 
25* 



292 TIIE YOUNG MECHANIC 

even half of this short time, is not spent in the 
labour of getting jargon by rote; each day 
some slight advance is made in the knowledge 
of tneir combinations. What we insist on is. 
that nothing be done to disgust the pupil : steady 
perseverance, with uniform gentleness, will in- 
duce habit, and nothing should ever interrupt 
the regular return of the daily lesson. II' ab- 
sence, business, illness, or any other cause, pre- 
vent the attendance of the teacher, a substitute 
must be appointed ; the idea of relaxation on 
Sunday, or a holiday, should never be permitted. 
In most public seminaries above one third, in 
some nearly one half, of the year is permitted 
to idleness : it is the comparison between severe 
labour and dissipation which renders learning 
hateful. Johnson is made to say, by one of his 
female biographers, that no child loves the per- 
son who teaches him Latin ; yet the writei 
would not take all the doctor's fame, and all 
the lady's wit and riches, in exchange for the 
hourly, unfeigned, unremitting friendship which 
he enjoys with a son who had no other master 
than his father. So far from being laborious or 
troublesome, he has found it an agreeable em- 
ployment to instruct his children in grammai 
and the learned languages. In the midst &f a 



THE LATIN LANGUAGE. 093 

variety of other occupations, hall' an hoir 
every morning for many years, during the time 
of dressing, has been allotted to the instruction 
of boys of different ages in languages, and no 
other time has been spent in this employment." 
It has been objected, that a classical educa- 
tion loses time in acquiring words only, when 
ideas ought to be acquired. This objection 
(though in a great measure unjust] would cer- 
tainly be without any colour of reason, if a 
plan could be proposed for uniting both these 
purposes ; if by a proper choice of books we 
could contrive to store the mmd at different 
periods with such useful, moral ideas as are 
adapted to its capacity. The first branch of sci- 
ence which youth is capable of comprehending 
appears to be history. On the knowledge of 
facts, all moral reasoning must depend; and 
facts learned in youth are certainly better re- 
tained than those which are acquired at any 
succeeding period. Young boys are not inte- 
rested in narrative (indeed there is hardly any 
other kind of composition which can engage 
them ;) and I have generally found them more 
delighted with true history and biography, if 
not prolix, than with poetry or novels. The 
tales of love, and the minutiae of private life 



294 rHE YOUNG MECHANIC. 

do not arrest their attention so much as the ad- 
ventures of heroes, and the vicissitudes of war. 
Now although learning be a business rathei 
than an amusement, certainly the more accept- 
able it can be made to the pupils, the better. 
On these principles, therefore, 1 would venture 
to deviate a little from the common order of 
school books, which schoolmasters are more 
anxious to select for the purity of the Latin, 
than for any real instruction or entertainment 
they contain. I would not be understood to 
insinuate, that the acquisition of the language, 
in the most perfect manner, is not a primary 
object; but I am of opinion " that at a time 
when books are read only to exemplify gram- 
matical rules, purity and elegance are not so 
much required, as when the scholar is more 
advanced." The initiatory books, I apprehend, 
have little influence in forming the taste ; before 
that effect can take place it is necessary to be 
master of the rudiments, to read the language 
with ease, and to be able to consider it with 
something of a critical eye. It may please the 
vanity of a parent to be told, that his boy is 
reading Virgil or Ovid ; and it may answer the 
master's own purpose, in a pecuniary view, to 
encourage this absurd vanity; bat in the mean 



THE LATIN LANGUAGE. 



29a 



time the real interest of the pupil is sacrificed 
For what can be more ridiculous, than to in 
volve a child, who is yet unacquainted with the 
lite ral meaning - of words, in all the obscurities 
of figurative and poetic diction ; and, before he 
lias acquired any ideas on common things, to 
expect that he should feel and admire the high- 
est efforts of the human imagination ? 

The books which I would recommend as 
proper to initiate children in the learned lan- 
guages, should be plain prose, simple, easy to 
be construed, and dispensing such knowledge 
as is adapted to their capacities. I would lead 
them by just gradations from unadorned lan- 
guage, and plain fact, to elegance of style, ele- 
vation of thought, and more abstract sentiment. 
After some very easy Latin, just sufficient to 
show them the nature of construing, I think 
Eutropius the most proper book. It is an 
abridgement of perhaps the most important 
series of events which the annals of the globe 
I can produce ; it is one of the easiest books to 
read, and the style is clear and perspicuous. 
After Eutropius, the young scholar may have 
an excellent taste of biography in the lives of 
Cornelius Nepos, which, in point of difficulty 
is properly the next step above Eutropius 



296 THE YC«.rG MECHANIC 

Justin may be read with the greatest advantage 
after thp other two: he is not remarkable for 
the beauty or elegance of his style; but l w 
collects so many useful tacts in the history .i 
mankind, and is, as ( can testify from expe- 
rience, so delightful a book to boys, that the 
advantages to be derived from the perusal of him 
infinitely counterbalances this objection. If the 
pupils caitnot go through the whole of these 
authors, the parts which they read may bp 
chosen so as to connect together, and afford 
them a general view of the progress and termi- 
nation of the principal states of antiquity. Let 
them next read the most interesting parts ol 
Caesar and Sallust, and some of Cicero's ora 
t:ons. A good set of the ancient maps oughi 
to be made use of while they are reading his- 
tory ; and thus Geography will be insensibly 
acquired, and more firmly implanted, than by 
any otner process. 

Until they can constiiie such Latin as Caesar's 
Commentaries tolerably fluently, without the aid 
of a dictionary, and have gone at least on c 
through a set of the common school exercises 
such as Bailey's, no other language, not even 
Greek, should interfere with the Latin ; other- 
wise the memory will be confused by the dif- 



THE LATIN LANGUAGE. 29? 

ferent grammars. But by the time they have 
finished the course of reading already specified. 
it is presumed they will be capable of under- 
standing the study of Greek. Their minds also 
will now be matured, and sufficiently cultivated 
to relish the charms of poetry, of which the 
iEneid is the chastest and most captivating spe- 
cimen. To the discretion of the master it may 
be left, how much of the ifoieki can be read at 
school with advantage. Somn of the moral 
Odes, all the unexceptionable Satires, and Epis- 
tles of Horace may follow, and a few of the 
Satires of Juvfcial ; varying occasionally ihe 
course of their studies by an oration of TuJly, 
the Cato Major, the Laelius, or the Offices. 
Ovid and Terence 1 will venture to proscribe* 
the former, because he inculcates licentious 
ness ; the latter, knavery. 1 know no spirit 
sooner caught by boys, than that little tricking 
disposition, that spirit of low cunning, which 
may be learned from some parts of this author. 
In the Comedies of Terence, the father is often 
i\ fantastic or an avaricious fool ; the son a pro- 
fligate ; and the servant, who is the cream of 
the jest, a complete villain. The purity of hia 
Latin, and the delicacy of his style, will not, in 
my estmiation, compensate for tiie danger which 



298 THE YOUNG MECHANIC. 

is incurred by the imitative faculties of youth. 
As for Ovid, there is another objection against 
him, for he corrupts the taste as well as the 
morals ; some part of the Metamorphoses may, 
however, be read with advantage.* 

Boys ought to read prose well before they 
meddle with the poets. The former has visibly 
so much the advantage of the latter, with re- 
spect to perspicuity and plainness of style, that 
I cannot but wonder how the latter came to 
take place of the former, in the common method 
of the schools. This looks something like 
teaching young children to stfnd upon their 
hands, before they know how to make use of 
their legs. Prose is necessary to teach them a 
proper Latin style ; for the reading of the poets 
can do them no kindness in this respect, but 
rather much hurt, if they be not first well ac- 
quainted with prose. The style of poetry is so 
remote from the ordinary manner of expres- 
sion, that to imitate it in prose, would be the 
most ridiculous thing in the world; and he 
would be sure to excite laughter, who should 
pretend to write a history in the strain of Vir- 
gil's /Eueid, or Horace's Lyrics. To preven 

• Gregory's Essays- 



1HE LATIN LANGUAGE. 29%, 

(herefore their confounding those two different 
Btyles, it will be necessary to make them read 
the historians well in the first place : by so 
doing, they will learn the genuine and proper 
signification of words, and use them accord- 
ingly : they will not be misled by the figurative 
use of words, phraseology, and forms of con- 
struction proper only for poetry ; nor need they 
fear to imitate the language of their authors ; 
whereas, in the reading of the poets, the case 
would be otherwise ; there they could borrow 
nothing, without rendering their style very 
bombastic and ridiculous.* 

The author of " Stemmata Latinitatis" has 
conferred an essential service on the public ; but 
still there is wanting a dictionary for schools, 
in which elegant and proper English might be 
substituted for the barbarous translations now 
in use. Such a dictionary could not be com- 
piled, we think, without an attention to the 
course of books which are most commonly 
used in schools. The first meanings given in 
the dictionary should suit the first authors 
which a boy reads; this may probably be a 
remote or metaphoric meaning : then the radical 



Clarke's Essay on Education, 1731). 
26 



300 TUB YOUNG MECHANIC. 

word should be mentioned, and it would noi 
cost a master any great trouble to trace the 
genealogy of words to the parent stock. 

Cordery is a collection of such mean sen- 
tences, and uninstructive dialogue, as to be 
totally unfit for boys. Commenius's " Visible 
World Displayed" is far superior, and might, 
with proper alterations and better prints, be- 
come a valuable English school book. Both 
these works were intended for countries where 
the Latin language was commonly spoken, and 
consequently they are filled with the terms ne- 
cessary for domestic life and conversation : for 
this very reason they are not good introduc- 
tions to the classics. Selections from Bailey's 
Phcedrus will be proper for young beginners on 
account of the glossary. We prefer this mode 
of assisting them with glossaries to the use of 
translations, because they do not induce indo- 
lent habits, and yet they prevent the pupil from 
having unnecessary labour. Translations always 
give the pupil more trouble in the end, than 
they save in the beginning. The glossary to 
Bailey's Phcedrus, which we have just mention- 
ed, needs much to be modernized, and the lan- 
guage requires to be improved. Mr. Valpy's 
Select Sentences would be far more useful i/ 



THE LATIN LANGUAGE 



30: 



they had a glossary annexed. As they are, 
they will however be useful after Phcedrus. 
Ovid's Metamorphoses, with all its monstrous 
faults, appears to be the best introduction to 
the Latin classics, and to heathen mythology. 
Norris's Ovid may be safely put into the hands 
of children, as it is a selection of the least ex 
ceptionable fables. Cornelius Nepos, a crab- 
bed book, but useful from its brevity, and from 
its being a proper introduction to Grecian and 
Roman history, may be read nearly at the same 
time with Ovid's Metamorphoses. After Ovid 
the pupil may begin Virgil, postponing some 
of the Eclogues, and all the Georgics.* 

To write exercises in Latin appears essential- 
ly necessary to grammatical perfection, and 
should commence as soon as the pupil has 
gone through the syntax. I do not feel con- 
vinced of the propriety or advantage of com- 
posing in verse. That several excellent writers 
had been accustomed to write Latin verses in 
their youth, is far from amounting to a proof in 
Its favour, because there is great probability, 
that those men would have excelled, whether 
they had written verses at school or not. That 



• Mr. K. L. Edgeworth. 



302 TIIE YOUNG MECHANIC. 

to write in verse facilitates and improves oui 
prose, I think admits of dispute. I am sure it 
cannot answer the end of accustoming the stu- 
dent to perspicuity and precision, or of perfect- 
ing him in grammar ; end I apprehend it will 
rather serve to induce a loose and vicious mode 
of composition, and lead him to attend more to 
sound than sense. It cannot be denied, that 
this practice takes up much more time than a 
common exercise ; and if it answer no particu- 
lar purpose, why waste that time, which might 
be more usefully employed in the acquisition 
of ideas ? The very mention of stringing 
words together without order or meaning, which 
is always the commencement, and too often 
the conclusion, of school versification, implies 
something ridiculous if not pernicious. But I 
will grant that a genius for poetry may receive 
some improvement from composing in verse 
when young ; whether that be a desirable con- 
sequence or not, those who are parents must 
determine. How few poets are so happy as to 
succeed ! and even when successful, how bar- 
ren, how uncertain are the rewards of genius ! 
The enthusiasm of poetry incapacitates us for 
most other employments, nor is the unsuccess- 
ful adventurer easily reduced to his sobei 



THE LATIN LANGUAGE. 303 

senses : lie contends in the face of poverty, ac- 
companied with contempt ; and pursues his itch 
of scribbling through innumerable disappoint- 
ments, without even the airy premium of ap- 
plause. I have heard it urged further, in de- 
fence of these poetic exercises, that they teacli 
boys quantity and pronunciation. But surely 
they never can be necessary on this account, if 
the master be careful from the first to accustom 
the learner to a right pronunciation ; and were 
not this sufficient, the end would be fully an- 
swered by a practice, which I think as salutary 
as the other is pernicious ; I mean that of com- 
mitting to memory some of the moral passages 
of Virgil, Horace, and the best of the poets. 
This will serve at once to furnish the mind with 
words and with ideas ; and will implant pre- 
cepts in the heart, which may be useful through 
all the different periods of life. If it cannot im- 
part, taste, it will improve it. It will infix in 
the mind the best rules of grammar in indelible 
characters.* 

It was with much regret that the compiler 
met with the following illiberal reflections b) 
the enlightened and ingenious Doctor Knox 



* Gregory's Essays 

26* 



304 TIIE YOUNG MECHANIC. 

" Some writers on the subject of educati )n 
have expressed themselves against the genera! 
practice of composing Latin verse at school^ 
with a degree of acrimony, which has led their 
readers to conclude, that they themselves were 
ignorant of the art, and without a taste for its 
beauties. I imagine too, that some of them 
never had a truly classical education at a public 
school, or were members of either English 
university." Liberal Education, page 65, edit. 
1783. Again, "Such objections appear very 
plausible to illiterate persons, and those very 
many who know not what a classical education 
means, or what advantages it tends to produce !'* 
Page 68. In the same work, page 284, Dr. 
Knox acknowledges, that Mr. Locke, who wrote 
decidedly against boys making verses at school, 
was a student of Christ Church College, Ox- 
ford ; and wrote there some Latin verses ad- 
dressed to Cromwell. But he also remarks, 
that " Locke was led to differ from others on 
Ihe subject of education from a warmth of re- 
forming spirit." Those assertions do not ap- 
pear well founded, for Locke produced his 
"Thoughts on Education" at the age of fifty - 
eight. It might therefore be said witli greater 
plausibility, that his decisions on this subject, 



THE GREEK LANGUAGE. 305 

were the result of much experience, mature 
judgment, and cool discrimination. 

The assertion will not perhaps be liable to 
be controverted by those, who are best ac- 
quainted with such subjects, and are best qua- 
lified to make extensive and just comparisons, 
if it be said that the Greek claims the supe- 
riority over all other languages. In its nume- 
rous mod-es of expression there is precision 
without obscurity, and copiousness without 
redundance. It owes the former to the various 
and diversified inflections of its words, and the 
latter to its great number of derivatives. In its 
general structure and formation, a pioper re- 
gard is paid to the ear, as well as to the under- 
standing ; for its energy and strength are not 
more striking than its harmony. The strict- 
ness of its rules does not impose too much re- 
straint upon its expressions, and its grammati- 
cal system is in every part exact and complete.* 

From a short view of its history and cha- 
racteristics, it will be evident, that this language 
deserves to be held up as a perfect model of 
expression, and that it fully justifies the praise 
of those scholars and critics, who have cele- 

* See Lord Monboddo on the Origin c c Language, vol 
*. page 25. 



306 THE YOUNG MECHANIC. 

orated its excellence in proportion as theyhavfe 
enjoyed its beauties, and derived taste, improve- 
ment, and pleasure, from the perusal of its in- 
comparable writers.* 

Greek is worth the pains of learning, merely 
as a language ; and I question whether any man 
can be an adequate judge of the structure, force, 
and harmony of language, who is totally igno- 
rant of it. The true principles of taste are to 
be imbibed in their greatest perfection from the 
Greek writers, whose chastity, perspicuity, and 
elegance, have never been excelled, and very 
seldom equalled. In teaching Greek, the most 
proper book to commence with is certainly one 
of the Gospels. I would prefer St. Matthew's, 
because I think it written in a more agreeable 
and entertaining manner than that of St. John, 
which is usually the first book. Of the New 
Testament, Matthew and Luke will be quite 
sufficient. After these I would recommend some 
easy prose ; perhaps the Pictures of Cebes would 
not be found too difficult. A few of the Odes 
of Anacreon, if selected with judgment, may 
be read. My predilection for History inclines 
me to recommend as much of Herodotus as may 

•Mr. Kett's Elements of General Knowledge. 



THE GREEK LANGUAGE 



307 



fionveniently be read. It is the most entertain- 
ing book I am acquainted with ; and much solici 
instruction may, on the whole, be collected 
from it. The style is simple and beautiful, with 
this additional circumstance in its favour, thai 
it is the best introduction to Homer. Some 
schoolmasters may prefer the Cyropeedia of 
Xenophon, which is an excellent book, if the 
boys do not think it prolix. It is almost need- 
less to mention, that the Anabasis is the best of 
all that author's works. After as much of 
Homer as may be thought expedient, it may be 
of use to dip a little into the Orations of Iso- 
crates, as introductory to Demosthenes, who 
must by no means be neglected. Of the Manual 
of Epictetus the master may, if he pleases, 
make considerable advantage, by taking occa 
sion to explain from it the moral philosophy of 
the Stoics. Thucydides, as well as Livy and 
Tacitus, the higher poets and philosophers, 
must, I fear, be reserved for the university ; as 
no school class can be expected to go through 
a greater number of books than those which I 
have already specified. By pursuing this plan 
of reading, I am persuaded the student would 
•eap much more useful knowledge, than by the 
tumbled, unsystematic method commonly pur- 



SOS THE YOUNG MECHANIC. 

sued in schools. What, perhaps, he would he. 
most deficient in, would be the heathen mytho- 
logy, of the great advantage of which I must 
confess myself ignorant. In return, he would 
be master of all the leading facts in the history 
of mankind ; and if history be to ethics what 
experiment is to physics, he would have laid 
the best foundation of moral reasoning. None 
of the advantages of classical learning, in re- 
spect to the improvement of taste, would be 
lost by this course of study ; and perhaps the 
style which would be formed from the authors 
I have recommended, would be preferable to 
the prettinesses which is acquired from reading 
poetry; being formed on the best models of 
that manly eloquence, which is the proper as- 
sociate and embellishment of virtuous princi- 
ples. I have omitted entering into a detail of 
the manner in which I would have the rudi- 
ments taught, because I do not in this respect, 
materially differ from the common practice of 
schools. Before a boy be put to construe, he 
should be well grounded in the Accidence, per- 
fectly master of the declensions of nouns and 
verbs, as well as the rules for determining the 
genders, and the formation of the tenses. Bu< 
1 do not think there is an absolute necessity 



THE GRE K LANGUAGE. 3QC\ 

previous to the reading of any author, to over 
charge his memory with a multitude of syntax 
rules, of the use and application of which he 
must be totally ignorant. The concords, and a 
few of the principal rules, will be quite enough 
for him when he begins to construe. He must 
afterwards continue to get off a portion of the 
other rules every day, and must be well exer- 
cised in the grammar during the whole of his 
progress. 

I agree with Mr. Knox, that to teach wholly 
by translations is pernicious. But I must ob- 
serve, that if with the first and second books 
which a child is put to construe, no translation 
be made use of, the master himself must be in 
place of a translation ; or the pupil must, at the 
expense of some of his pocket money, apply 
to his school-fellows. It is impossible, on the 
first efforts to construe, to proceed without some 
guide ; or to use a dictionary with that ease 
and dexterity which are essential to profit. To 
allow them the assistance of a translation at 
first, and before they have acquired a little stock 
of words, is more suitable to the progressive 
powers of the human mind. I grant there will 
be some difficulty to be surmounted when they 
Jirst lay aside the translation ; but this will bd 



310 TIIE YOUNG MECHANIC. 

nothing like so discouraging as the gloomy 
prospect of entering on a language totally un 
known, and being obliged to consult a die* 
tionary for every word.* 

The modern practice of teaching Greek 
through the medium of Latin appears to me 
highly erroneous. It not only retards the pro- 
gress of a scholar, but it renders the idioms of 
both languages confused ; and the beauty of the 
article, and some of the tenses, independent of 
other considerations, is thus entirely lost. The 
labours of literary men cannot be directed to a 
more useful purpose, than the compilation of 
dictionaries and grammars in the Greek and 
vernacular tongues.f 

To the objection that too much time is lost 
in learning the words of the sentiments which 
we might obtain by means of translations, this 
plain answer may be given, that a person can 
never learn a language, without adding to the 
stock of his ideas ; and that the better the lan- 
guage is, (and where shall we find any equal to 
the Greek and Latin ?) the more correct will be 
the judgment, and the more vigorous the per- 
ceptions of the learner. The learned tonguei 

* Gregory's Essays. f Northmore- 



CLASSICAL LEARNING. 3^ 

form at once, even considered merely in then 
structure, the best code of laws for taste, and 
(he best models for logical reasoning and argu- 
ment. No one who can read the classics would 
exchange the fruit of the time spent upon them 
for any other attainment which his earlier years 
could have made.* 

The Earl of Chatham says to his nephew, 
u I rejoice to hear that you have begun Homer's 
Iliad ; and have made great progress in Virgil ; 
I hope you taste and love these authors parti- 
cularly. You cannot read them too much , 
they are not only the two greatest poets, but 
they contain the finest lessons for your age to 
imbibe : lessons of honour, courage, disinte- 
restedness, love of truth, command of temper, 
gentleness of behaviour, humanity, and in one 
word, virtue, in its true signification. Go on, 
my dear nephew, and drink as deep as you can 
of these divine springs : the pleasure of the 
draught is equal at least to the prodigious ad- 
vantages of it to the heart and morals."}* 

There is yet wanting in different languages, 
says Stevenson, initiatory books, containing 

• Edinburgh Review, iii. 351. 

-j- Letters to T. Pitt, Esq., afterwards Lord Camelford, 
page 6. 

27 



312 THE YOUNG MECHANIC. 

physical facts, none of which would be dry and 
uninteresting. Natural History and Philosophy, 
in all their branches, even though they were 
superficial, would be of much greater use in 
every situation in life, than an intimacy with 
poetic flights of imagination, and all the lumber 
of the heathen mythology, the perusal of which 
affords but selfish, momentary, and insulated 
pleasure. Young people remember facts much 
more readily than sublime metaphor, or labour- 
ed sentiment.* 

Though I particularly recommend classical 
learning, says Dr. Knox, I do not recommend 
it exclusively. I think it ought to claim the 
earliest attention, and to form the foundation ; 
because no other learning contributes so much 
to open and to polish the mind. After this 
polish and expansion are acquired, and this 
foundation laid, 1 recommend an attention to 
the sciences, to natural history and experimental 
philosophy, to botany, to chemistry, to paint- 
ing, to architecture, to mechanical works, and 
in general to all the productions of human in- 
genuity. A capacious mind will view the uni- 
rerse and all which it contains, as one vast 

• Remarks on the inferior utility of Classical Lewning 



MATHEMATICS. ^Id 

volume laid before it for perusal. Philology 
alone is comparatively a confined, though ele- 
gant attainment. 

MATHEMATICS. 

Arithmetic may now be considered as having 
advanced to a degree of perfection which in 
former times could scarcely have been con- 
ceived, and to be one of those few sciences 
which have left little room for farther improve- 
rnsnt. It is, however, a serious and almost 
general complaint, that few children, while at 
school, make any tolerable progress in arith- 
metic ; and that the generality, after having 
spent several years under the tuition of a mas- 
ter, are incapable of applying the few rules 
which they have learned, to the useful purposes 
of life. A few elementary principles are ac- 
quired by rote, and therefore quickly forgotten ; 
because the most essential particulars, namely, 
the reasons on which these rules are founded, 
and their extensive use in the various concerns 
of society are generally omitted.* 

So much of the science of numbers as is in 
common use, as the numeration, subtraction, 

* Dom. Encyclopaedia. 



314 THE YOUNG MECHANIC. 

multiplication, and division of money, should 
be learnt with accuracy; to which should be 
added the rule of three and decimal fractions ; 
which will abundantly repay the labour of ac- 
quiring them by the pleasure and utility which 
will perpetually result from the knowledge of 
them through life.* 

The only sciences which can be denominated 
pure are the Mathematics. Of these, every 
mechanic and labourer should be made ac- 
quainted with Euclid, particularly the first six 
books ; also algebra ; the properties of the conic 
sections ; and the doctrine of fluxions. Owing 
to the very little attention which is paid to these 
sciences at present, it may appear to many, that 
their study is attended with great difficulty, and 
little advantage. Neither of these prejudices 
Dorders on the confines of truth. In order 
that those sciences may become capable of gra- 
tifying the desire which children entertain foi 
the acquisition of truth and knowledge, i„ is 
absolutely necessary that they be rendered as 
clear and evident as possible, and also that 
their application and utility be made apparent. 
Nothing more seems wanting to render the 
study of mathematics pleasant and agreeable, 
* Dr. Darwin. 



MATHEMATICS. 21i 

than to apply them to those purposes wnieb 
must make their utility and perfection clear 
striking, and interesting. The time in which 
mathematics should be studied, must succeed 
that of literature. To comprehend abstract and 
general truth, some energy and comprehension 
of mind are requisite. To point out the pre- 
cise period when the study of mathematical 
science should commence, is attended with some 
difficulty. It must evidently vary, according 
to the progress which the mind may have made 
towards maturity and perfection.* 

I agree with Mr. Locke, that there is no study 
better fitted to exercise and strengthen the rea- 
soning powers, than that of the mathematical 
sciences, for two reasons ; first, because there 
is no other branch of science which gives such 
scope to long and accurate trains of reasoning , 
and, secondly, because in mathematics there is 
no room for authority, nor for prejudice of any 
kind, which may give a false bias to the judg- 
ment. When a youth of moderate parts begins 
to study Euclid, every thing at first is new to 
him. His apprehension is unsteady; his judg« 
ment is feeble, and rests partly upon the evi« 
dence of the thing, and partly upon the authority 

27* * Dr - Covvan - 



316 



THE YOUNG MECHANIC. 



of his teacher. But every time he goes ovei 
the definitions, the axioms, the elementary pro- 
positions, more light breai^ in upon him : the 
language becomes familiar^ and conveys clear 
and steady conceptions ; the judgment is con- 
firmed; he begins to see what demonstration 
is ; and it is impossible to see it without being 
charmed with it. He perceives it to be a kind 
of evidence which has no need of authority to 
strengthen it. He finds himself emancipated 
from that bondage ; and exults so much in this 
new state of independence, that he spurns at 
authority, and would have demonstration for 
every thing ; until experience teaches him, that 
this is a kind of evidence which cannot be had 
in most things ; and that in his most important 
concerns, he must rest contented with probabi- 
lity. As he goes on in mathematics, the road 
of demonstration becomes smooth and easy ; 
he can walk in it firmly, and take wider steps : 
and at last he acquires the habit, not only ol 
understanding a demonstration, but of discover- 
ing and demonstratirT mathematical truths. 
Thus, a man, without uiles of logic, may ac- 
quire a habit of reasoning justly in mathema 
tics ; and, I believe he may, by like means, ac- 
quire a nabit of reasoning justly in mechanics, 



logic. 317 

in jurisprudence, in politics, or in any other 
science. 

LOGIC. 

Good sense, good examples and assiduous 
exercise, may bring a man to reason justly and 
acutely in his own profession, without rules. 
But if any man think, that from this concession 
he may infer the inutility of logic, he betrays a 
great want of that art by this inference : for it 
is no better reasoning than this, that because a 
man may go from Edinburgh to London by the 
way of Paris, therefore any other road is use- 
less. There is perhaps no mechanic art which 
may not be acquired, in a very considerable de- 
gree, by example and practice, without reducing 
it to rules. But practice, joined with rules, 
may carry a man on in his art farther and more 
quickly, than practice without rules. Every 
ingenious artist knows the utility of having his 
art reduced to rules, and by that means made a 
science. He is thereby enlightened in his prac- 
tice, and works with paore assurance. By rules, 
he sometimes corrects his own errors, and often 
detects the errors of others : he finds them of 
great use to confirm his judgment, to justify 
what is right, and to condemn what is wrong 



318 THE YOUNG MECHANIC. 

Is it of no use in reasoning, to be well acquainted 
with the various powers of the human under- 
standing, by which we reason ? Is it of no 
use, to resolve the various kinds of reasoning 
into their simple elements ; and to discover, as 
far as we are able, the rules by which these 
elements are combined in judging and in rea- 
soning ? Is it of no use, to mark the various 
fallacies in reasoning, by which even the most 
ingenious men have been led into error ? It 
must surely betray great want of understanding, 
to think these things useless or unimportant. 
These are the things which logicians have at- 
tempted, and which they have executed ; not 
indeed so completely as to leave no room for 
improvement, but in such a manner as to give 
very considerable aid to our reasoning powers. 
That the principles laid down with regard to 
definition and division, with regard to the con- 
version and opposition of propositions and the 
general rules of reasoning, are not without use, 
is sufficiently apparent from the blunders com* 
mitted by those who disdain any acquaintance 
with them.* 

Geometry should always form a part of a 

* Lor J Kaimes' Sketches. 



LOGIC 3j£ 

iberal course of studies. Jt has its direct uses 
and its indirect. It is of great importance foi 
the improvement of mechanics and the arts of 
life. It is essential to the just mastery of as- 
tronomy and various other eminent sciences 
But its indirect uses are perhaps of more worth 
than its direct. It cultivates the powers of the 
mind, and generates the most excellent habits. 
It eminently conduces to the making man a 
rational being, accustoms him to a closeness of 
deduction, which is not easily made the dupe 
of ambiguity, and carries on an eternal war 
against prejudice and imposition.* But geome- 
try is not a competent guide to the art of rea- 
soning without the study of logic. 

It is a very great error to suppose that logic 
consists only in those formal debates and ver- 
bal disputations, in which the schoolmen and 
their fo lowers consumed so much time in the 
dark agts, previous to the revival of classical 
learning. It is equally a mistake to imagine, 
that it is merely intended to teach the method 
of disputing by rules, and to instruct a person 
to converse, not from a love of truth, but a 
desire of victory. As there is nothing more 

• Godwin's Enquirei. 



320 THE VOUNG MECHANIC. 

disingenuous than such a conduct as this, no 
thing more unbecoming a rationable being, than 
to oppose sophistry to good sense, and evasion 
to sound argument, the logician disclaims this 
abuse of the principles of his art, and vindi- 
cates its rights by displaying its true and propei 
office. It is in reality capable of affording the 
most important assistance to the understanding 
in its inquiries after truth ; it is eminently use- 
ful in the common affairs of life, and renders 
the greatest service to science, learning, virtue, 
and religion. 

Logic is the art of forming correct ideas, and 
of deducing right inferences from them ; or it 
may be said to constitute the knowledge of the 
human mind, inasmuch as it traces the progress 
of all our information, from our first and most 
simple conception of things, to those numerous 
conclusions which result from comparing them 
together. It teaches us in what order our 
thoughts succeed each other, and it instructs ua 
in the relation which subsists between our 
ideas, and the terms in which we express them 
It distinguishes their different kinds, and points 
out their properties ; discovers the sources of 
our intellectual mistakes, and shows how we 
may correct and prevent them. It displays 



logic. 321 

those principles and rules, which we follow, 
although imperceptibly, whenever we think in 
a manner conformable to truth. 

The faculty of reason is the pre-eminent 
quality, by which mankind are distinguished 
from all other animals ; but still we are far from 
finding that they possess it in the same degree. 
There is indeed as great an inequality in this 
respect in different persons, as there is in their 
strength and agility of body. Nor ought this 
disproportion to be wholly ascribed to the 
original constitution of the minds of men, or 
the difference of their natural endowments ; for, 
if we take a survey of the nations of the world, 
we shall find that some are immersed in igno- 
rance and barbarity, others enlightened by 
learning and science ; and, what is still more 
remarkable, the people of the same nation have 
been in various ages distinguished by these 
very opposite characters. It is, therefore, by 
due cultivation, and proper diligence, that we 
increase the vigour of our minds, and cairy 
reason to perfection. Where this method is 
followed, the intellect acquires strength, and 
knowledge is enlarged in every direction ; where 
it is neglected, we remain ignorant of the value 
M' our own powers; and those faculties, by 



322 THE YOUNG MECHANIC. 

which we are qualified to survey the vast fabric 
of the world, to contemplate the whole face of 
nature, to investigate the causes of things and 
to arrive at the most important conclusions as 
to our welfare and happiness, remain buried in 
daikncss and obscurity. No branc i of science 
therefore affords us a fairer prospect i f improve- 
ment, than that which relates to the understand- 
ing, defines its powers, and shows the method 
by which it acquires the stock of ks ideas, and 
accumulates general knowledge.* 

C©MPOSITION. 

When we are employed after a proper man- 
ner, in the study of composition, we are culti- 
vating season itself. True rhetoric and sound 
logic are very nearly allied. The study of ar- 
ranging and expressing our thoughts with pro- 
priety, teaches us to think, as well as to speak, 
accurately. By putting our sentiments into 
words we always conceive them more distinctly. 
Every one who has the slightest acquaintance 
with composition knows, that when he ex- 
presses himself ill on any subject, when his 
arrangement is loose, and his sentences become 

* Mr. Rett's Elements. 



composition 323 

feeble, the defects of his style can, almost on 
every occasion, be traced back to his indistinct 
conception of the subject : so close is the con- 
nection between thoughts and the words in 
which they are clothed. The study of com- 
position, important in itself at all times, has 
acquired additional importance from the taste 
and manners of the present age ; an age wherein 
improvements, in every part of science, have 
been prosecuted with ardour. To all the libe- 
ral arts much attention has been paid ; and to 
none more than to the beauty of language, and 
the grace and elegance of every kind of writing. 
The public ear is become refined. It will not 
easily bear what is slovenly and incorrect. 
Every one who writes must aspire to some merit 
in expression, as well as in sentiment, if he 
would not incur the danger of being neglected 
and despised. I will not deny that the love of 
minute elegance, and attention to inferior orna- 
ments of composition, may have engrossed too 
great a degree of the public regard. It is in- 
deed my opinion, that we lean to this extreme ; 
often more careful of polished style, than of 
storing it with thought. Yet hence arises a 
new reason for the study of just and proper 
composition. If it be requisite *io f to be den- 
28 



324 THE YOUNG MECHANIC. 

cient ill elegance and ornament, in times when 
they are in such high estimation, it is still more 
requisite to attain the power of distinguishing 
false ornament from true, in order to prevent 
our being carried away by that torrent of false 
and frivolous taste, which never fails, when it 
is prevalent, to sweep along with it the raw and 
the ignorant. They who have never studied 
eloquence in its principles, nor have been trained 
*o attend to the genuine and manly beauties of 
good writing, are always ready to be caught by 
the mere glare of language ; and when they 
come to speak in public, or to compose, have 
no other standard on which to form themselves, 
except what chances to be fashionable and po- 
pular, how corrupted soever and erroneous that 
may be.* 

Though I have advised the pupil to exercise 
himself in composition, yet I will also caution 
him against the itch of scribbling. Let him 
never take the pen in hand, nor place the paper 
before him, till he has bestowed much time and 
deep thought on the subject. To the want of 
this previous attention we owe the numerous 
productions which disgrace letters, and which 
die almost as soon as they are brought forth ; 
* Dr. Blair's Lectures. 



IMPROVEMENT OF MEMORY. 305 

tvhicii, like weeds in a garden, spring- up luxu- 
riantly without cultivation, which are useless 
or noisome, and which only serve to impede 
the growth of salutary plants and pleasant 
flowers. Pretenders arise in every department, 
and disgrace it. Let the liberal and solid scholar 
attend to the circumstances of time and place, 
in the modest display of his attainments. It is 
unmanly timidity to conceal them on proper 
occasions ; it is ridiculous arrogance to intrude 
on unwilling and injudicious observers. Mo- 
desty is the characteristic of real merit ; and 
firmness, of conscious dignity. The man of 
sense will be diffident, but at the same time will 
have spirit enough to repel the insolent attacks 
of ignorance and envy.* 

IMPROVEMENT OF THE MEMORY. 

The following observations, if attended to, 
may greatly assist those more advanced in life, 
in strengthening the memory. 1. Let the stu- 
dent never quit any branch of study till he be 
perfectly master of it, and can comprehend it 
as a whole, as well as in parts. 2. Endeavour 
to link and connect the leading ideas, to class 
facts, and arrange them under different heads ; 
♦Dr Knox. 



326 THE YOUNG MECHANIC. 

so that the mind shall be able at one view to 
recall the outlines of the whole science, and af- 
terwards to pa^ss to the inferior branches, or sub- 
divisions. The ancients formed their memories 
almost entirely by this method; and indeed 
memory can never be useful without system 
3. Never commit mere words to memory as 
substitutes for true knowledge. Many a young 
person forgets what he has been taught because 
he never understood it. This is the true reason 
why boys make so wretched a proficiency in 
attaining the Latin language, unde/ masters who 
give them page after page of old Lilly to com- 
mit to memory, without the occurrence of a 
question or an explanation. In this manner 
they are also taught their catechisms, the ideas 
in which are infinitely above their comprehen- 
sion. 

The first thing which strikes us, in looking 
over Dr. Franklin's works, is the variety of his 
observations on different subjects. We might 
imagine, that a very tenacious and powerful 
memory was necessary to register them ; but 
Dr. Franklin informs us, that it was his con- 
stant practice to note down every thing as it 
occurred to him : he urges his friends to do the 
same ; he observes, that there is scarcely a day 



IMPROVEMENT OF MEMORY. 22\ 

passes without our hearing or seeing something, 
which, if properly attended to, might lead to 
useful discoveries. By thus committing his 
ideas to writing, his mind was left at liberty to 
think. No extraordinary effort of memory 
was, even on the greatest occasions, requisite.* 
On the whole, the most effectual way to ac- 
quire a good memory is by constant and mo- 
derate exercises of it ; for the memory, like 
other habits, is strengthened and improved by 
daily use. It is scarcely credible to what a de- 
gree both active and passive memory may be 
improved by long practice. ScaHger reports 
of himself that in his youth he could repeat 
above one hundred verses, having but once 
read them ; and Boethius declares, that he wrote 
his comment on Claudian without consulting 
the text. The extraordinary memory of Ma- 
gliabechi is well known. That of Jediah Bux- 
ton was of a peculiar kind ; so long was it 
habituated to numbers, that it could fix on 
nothing else. To hope, however, for such de- 
grees of memory as these, would be equally 
vain as to hope for the strength of Hercules, or 
the swiftness of Achilles. There are clergy* 



* Chiefly by Miss Edgeworth. 

28* 



328 THE YOUNG MECHANIC. 

men who can get a sermon by heart in tw« 
hours, though their memory when they began 
to exercise it, was rather weak than strong : and 
pleaders, with other orators, who can speak in 
public extempore, often discover, in calling in- 
stantly to mind all the knowledge necessary on 
the present occasion, and every thing of im- 
portance which may have been advanced in the 
course of a long debate, such powers of reten- 
tion and recollection as, to the man who has 
never been obliged to exert himself in the same 
manner, are altogether astonishing. As habits, 
in order to be strong, must be formed in early 
life, the memories of children should therefore 
be constantly exercised ; but to oblige them 
to commit to memory what they do not under* 
stand, prevents their faculties, and gives them a 
dislike to learning. In a word, those who have 
most occasion for memory, as orators and pub- 
lic speakers, should not suffer it to lie idle, but 
constantly employ it in treasuring up and fre~ 
quently reviving such things as may be of most 
importance to them ; for by these means, it will 
be more at their command, and they may place 
greater confidence in it on any emergency.* 

* The Idler. 



NATURAL PHILOSOPHY. £29 

CHAPTER XI. 
THE MECHANIC'S STUDIES CONTINUED. 

Natural Philosophy is commonly defined 
to be that art or science which considers the 
powers and properties of natural bodies, and 
their mutual action on each other. Moral 
Philosophy relates to whatever concerns the 
mind and intellect; Natural Philosophy, on the 
other hand, is only concerned with the material 
part of the creation. The moralist's business 
is to inquire into the nature of virtue, the 
causes and effects of vice, to propose remedies 
for it, and to point out the mode of attaining 
happiness. The naturalist, on the contrary, 
has nothing to do with spirit ; his business is 
confined to body or matter. The first and 
principal part of this science is to collect all the 
manifest and sensible appearances of things, 
and reduce them into a body of Natural History. 

Natural Philosophy differs from Natural 
History in its appropriated sense, the business 
of the latter is only to observe the appearance 
of natural bodies separately, and from these 



330 THE YOUNG MECHANIC. 

appearances to class them with other bodies to 
which they are allied. Natural Philosophy 
goes farther, and recites the action of two 01 
more bodies upon each other ; and though it 
can neither investigate nor point out the causes 
of those effects, whatever they be, yet from 
mathematical reasoning combined with expe- 
rience, it can be demonstrated, that in such cir- 
cumstances such effects must always take place 

Natural Philosophy, till lately, has been di- 
vided into four parts, commonly called the fom 
branches, viz. — 1. Mechanics ; 2. Hydrostatics ; 
3. Optics ; and 4. Astronomy ; and these again 
subdivided into many parts. Modern discove- 
ries have added, however, two more parts, viz., 
1. Magnetism; 2. Electricity and Galvanism. 
Every one is acquainted with the benefits derived 
from the sciences of Mechanics, Hydrostatics, 
and Hydraulics, to which we are indebted for 
many useful inventions. Among these are wind 
and water mills, aqueducts, pumps, fire engines, 
steam engines, &c, &c. 

Pneumatics supply, even to a superficial en- 
quirer, much instruction and amusement. Sure- 
ly all are interested in the nature and properties 
of a fluid which is necessary to every moment 
of our existence. 



NATURAL PHILOSOPHY. 33 

How great would have been the surprise of the 
ancients, could they have conceived the effects 
which are now produced by the reflection and 
refraction of light ! By a skilful management 
of these properties, telescopes, and various 
optical instruments are constructed. Objects 
too remote to be perceived by the naked eye, 
are enlarged and rendered visible. The satel- 
lites of Jupiter and Saturn, the mountains and 
cavities in the moon, and the changes which 
take place on the sun's disc, are thus discover- 
ed, and afford subject for admiration and in- 
quiry. Neither is the delightful scene of Optics 
confined to the contemplation of distant objects. 
Minute animals, the vessels of plants, and, in 
short, a new world in miniature is disclosed to 
our view by the microscope, and an inexhaus- 
tible fund of rational entertainment and know- 
ledge is brought within the spere of our senses. 

Of all the sciences to which geometry im- 
parts the solidity of its principles, and the 
clearness of its proofs, the most beautiful and 
the most sublime is Astronomy. This is per- 
haps the most exact and most definite part of 
natural philosophy : for it rectifies the errors 
of sight, with respect to the apparent motions 
of the planets ; explains the just dimensions, 



332 THE YOUi\G MECHANIC 

relative distances, due order, and exact propor- 
tions of the spherical bodies, which compose 
the solar system. Nor is it even confined to 
these great objects of nature, since it opens the 
stupendous prospect of other suns, and other 
systems of planets, scattered over the bound- 
less fields of space, and moving in obedience 
to their respective laws. It marks out their 
particular places, assigns their various names, 
and classes all the systems of worlds in their 
respective constellations. The calculations of 
astronomy prove the certainty of the future 
phenomena of the heavenly bodies, when the 
eccentric comet will reappear, after having tra- 
versed the most distant regions of the heavens, 
or at what point of time the bright luminaries 
of day and night will be immersed in the par- 
tial, or total darkness of an eclipse. 

CHEMISTRY. 

As soon as man begins to think, and to rea- 
son, the different objects which surround him 
on all sides naturally engage his attention. 
\fter being astonished at the wonders of the 
atmospheric and higher regions, he cannot fail 
-o be struck with the number, diversity, and 
oeauty of those on earth, and naturally feels a 



CHEMISTRY 335 

desire to be better acquainted with their proper- 
ties and uses. If he reflect also, that he him- 
self is altogether dependent on these objects, 
not merely for his pleasures and comforts, but 
for his very existence, this desire must become 
irresistible. Hence that curiosity, that eager 
thirst for knowledge, which animates and dis- 
tinguishes generous minds. 

As a science, chemistry is intimately con- 
nected with all the phenomena of nature ; the 
causes of rain, snow, hail, dew, wind, earth- 
quakes ; even the changes of the seasons can 
never be explored with any chance of success 
while we are ignorant of chemistry : and the 
vegetation of plants, and some of thfl most im- 
portant functions of animals, have received all 
their illustration from the same source. No 
study can give us more exalted ideas of the 
wisdom and goodness of the eternal cause than 
this. As an art, it is intimately connected with 
all our manufactures : the glass-blower, the 
potter, the smith, and every other worker in 
metals ; the tanner, the soap-maker, the dyer, 
the bleacher, are practical chemists ; and the 
most essential improvements have been intro- 
duced into all these arts by the progress which 
chemistry has made as a science. Agriculture 



334 THE YOUNG MECHANIC. 

can only be improved rationally, and certainly 
by calling in the assistance of chemistry ; and 
the advantages which medicine has derived 
from the same source, are too obvious to be 
pointed out.* 

NATURAL HISTORY. 

I am convinced, says Rousseau, that at all 
times of life, the study of nature abates the 
taste for frivolous amusements, prevents the 
tumult of the passions, and provides the mind 
with a nourishment which is salutary, by filling 
t with objects most worthy of its contempla 
tion. 

Of all the studies in which the minds o? 
youth may be employed, none, perhaps, deservi 
more strongly to be recommended, than thos* 
of natural history and physics. The object* 
on which they are occupied being such as com' 
under the cognizance of our senses, they ar v 
more easily comprehended by the juvenile up 
derstanding, than the refinements of grammar 
o! the abstract ideas of moral philosophy : ?• 
the same time, they afford an inexhaustible tunc' 
i\' entertainment; and their great utility rr 

* Thomson's Chemistry. 



NATURAL HISTORY. 33s 

sivery situation in life is universally acknow 
ledged.* 

It is the glorious privilege of man, while 
other animals are confined within the limits 
which instinct has prescribed, to carry his 
servationa beyond his own immediate wai 
and to contemplate the universe at large. He 
extends his inquiries to all the objects which 
sin round him; exercises his judgment, and in- 
forms his understanding, by ascertaining their 
nature, properties, and uses. In the various 
branches of mathematics, in the abstract specu- 
lations of metaphysics, or in searching the re- 
cords of history, he is solely intent on the opera- 
tions of his own mind, or the actions of him- 
self and his fellow creatures : but in the study 
of nature, he examines every object presented 
to his senses, and takes a general survey of the 
wide and interesting prospect of the creation. 
The earth he treads, the ocean he crosses, the 
air he breathes, the starry heavens on which he 
gazes, the mines and caverns he explores, all 
present to him abundant materials for his ic- 
searches. And, when thus employed, he is 
engaged in a manner peculiarly suitable to his 

* Preface to Pleasinir Pieccptor. 

29 



336 sG MECHANIC. 

faculties, since he alone is capable of know- 
ledge, he alone is distingiflshed by the power 
of admiration, and exalted by the faculty of 
reason. The terraqueous globe presents a most 
glorious and most sublime prospect, equally 
worthy of the capacity of man to contemplate, 
and beautiful to his eye to behold. And the 
treasures of nature, which this prospect com- 
prehends, are so rich and inexhaustible, that 
they may furnish employment for his greatest di- 
ligence, stimulated by the most ardent curiosity 
and assisted by the most favourable opportuni- 
ties. At the same time that she solicits him to 
follow her, not only in her open walks, but 
likewise to explore her secret recesses, she fails 
not to reward him with the purest gratifications 
of the mind, because at every step he takes, 
new instances of beauty, variety, and perfection 
are unfolded to his view. 

The study of the works of nature is in itself 
capable of affording the most refined pleasure, 
and the most edifying instruction. All the ob- 
jects with which we are surrounded, the small- 
est as well as the greatest, teach us some useful 
lesson. All of them speak a language directed 
to man, and to man alone. Their evident ten- 
dency to some determined cjh!, marks the de 



NATURAL HISTORY. 337 

sign of a great Creator. The volume of crea- 
tion contains the objects of arts, science, and 
philosophy, and is open to the inspection of all 
the inhabitants of the globe.- Nature speaks 
by her works an universal language, the rudi- 
ments of which are peculiarly adapted to the 
inclination and capacity of the young, whose 
curiosity may be gratiiied and excited by turns ; 
but more profound and extensive inquiries are 
suitable to the contemplation of persons of 
every age ; and no subjects can be more worthy 
of their attentive observation.* 

A walk in the fields, after reading a little in 
natural history, may furnish opportunities of 
important instruction. The hills, the dales, and 
quarries afford matter of speculation on their 
formation, use, and beauty. And this may be 
rendered intelligible to a child, by a person 
who really understands the subject, and is not 
a mere pedant who has only committed techni- 
cal words to memory. So in all probability 
may every branch of real knowledge. Those 
branches which are now lost to common sense 
by calculations and mathematical processes, are 
not always, if they be ever understood by those 

* Mr. Kelt's Elements. 



338 THE YOUNG MECHANIC. 

who profess to understand them. Every tiling 
which is not applicable to use, and the applica- 
tion of which cannot be made obvious to com- 
mon sense, is gothic jargon, and not science , 
and people who glory in such acquisitions have 
not a clear and good idea of what constitutes 
real knowledge. This explains the problem, 
why, in the present state of learning, there are 
no plain, intelligible, and easy methods of teach- 
ing the sciences, and so few good elementary 
books. The reason is, that the sciences are 
not generally and thoroughly understood. Every 
man can easily teach another what he perfectly 
understands himself. But if half his terms be 
merely technical, and he can give no definitions 
of them which convey ideas, it is no wonder 
that learning is difficult, as it is always painful 
to commit to memory words which have no 
meaning j and all the progress made upon such 
foundations is ever attended with that anxiety 
and anguish, which have so strongly marked 
the countenances of our philosophers. In the 
same manner as the general truths ot natural 
history might be occasionally exemplified in 
the fields, many of the mathematic, astronomic, 
and particularly the mechanic problems, migh* 
be examined in a walk. This would not onl) 



NATURAL HISTORY. 



►39 



6e ^esent instruction, but bring the pupil into 
a habit of having an object and a view in every 
action. He would not then experience the 
common unhappiness of not knowing what to 
do with himself; or when he has determined 
on a walk or a ride, be miserable for want of 
being able to determine where to g A or witii 
what object to engage his thoughts * 



340 THE YOUNG MECHANIC. 

CHAPTER XII. 
THE MECHANIC'S STUDIES CONTINUED 

HISTORY. 

Curiosity is one of the strongest and mosl 
active principles of human nature. Through- 
out the successive stages of life, it seeks with 
avidity for those gratifications, which are con- 
genial with the different faculties of the mind. 
The child, as soon as the imagination begins to 
open, eagerly listens to the tales of his nurse : 
the youth, at a time of life, when the love of 
wliat is new and uncommon is quickened by 
sensibility, is enchanted by the magic of ro- 
mances and novels : the man, whose mature 
judgment inclines him to the pursuit of truth, 
applies to genuine history, which even in old 
age continues to be a favourite object of his at- 
tention ; since his desire to be acquainted witli 
the transactions of others has nearly an equal 
power over his mind with the propensity to 
relate what has happened to himself 

History, considered with respect to the nature 
v,f its subjects, may be divided into general and 



HISTORY. 34] 

particular; and with respect to time, into an- 
cient and modern. Ancient history commences 
with the creation, and extends to the reign of 
Charlemagne, in the year of our Lord 800. 
Modern history, beginning with that period, 
readies down to the present times. General 
history relates to nations and public affairs, and 
may be subdivided into sacred, ecclesiastical, 
and profane. Biography, memoirs, and letters, 
constitute particular history. Statistics refer to 
the present condition of nations. Geography 
and Chronology are important aids, and give 
order, regularity and clearness to them all. 

To draw the line of proper distinction be- 
tween authentic and fabulous history, is the 
first object of the discerning reader. Let him 
not burden his memory with events which 
ought perhaps to pass for fables; let him not 
fatigue his attention with the progress of em- 
pires, or the succession of kings, which are 
thrown back into the remotest ages. He will 
find that little dependence is to be placed upon 
the relations of those affairs in the Pagan 
woild, which precede the invention of letters, 
and were built upon mere oral tradition. Let 
him leave the dynasties of the Egyptian kings, 
the expeditions of Sesostris, Bacchus, and Jason, 



342 THE YOUNG MECHANIC. 

and the exploits of Hercules and Theseus, foT 
poets to embellish, or chronologists to arrange. 
The fabulous accounts of these heroes of anti- 
quity may remind him of the sandy deserts, 
lofty mountains, and frozen oceans, which arc 
laid down in the maps of the ancient geogra- 
phers, to conceal their ignorance of remote 
countries. Let him hasten to firm ground, 
where he may safely stand, and behold the 
striking events, and memorable actions, which 
the light of authentic records display to his 
view. They alone are amply sufficient to en- 
rich his memory, and to point out to him well 
attested examples of all that is magnanimous, 
as well as of all that is vile ; of all that debases, 
and all that ennobles mankind.* 

Unfortunately the study of history is not 
without its dangers and inconveniences of va- 
rious kinds. It is a very difficult matter to 
place one's self in such a point of view as to 
be able to judge equitably of our fellow crea- 
tures. It is one of the common vices of his- 
tory to paint man in a disadvantageous rather 
than in a favourable light. Revolutions and 
fatal catastrophes being most interesting, so long 
as a people have continued to increase and 
* Mr. Rett's Elements. 



HISTORY 



34! 



prosper in the calm of a peaceab.e government 
history has remained silent ; it speaks of na- 
tions only when, growing insupportable to 
themselves, they begin to interfere with their 
neighbours, 01 to suffer their neighbours to in- 
terfere with them. We are favoured with very 
exact accounts of those nations which verge 
towards destruction ; but of those which have 
been flourishing, we have no history ; they 
have been so wise and happy as to furnish no 
events worth recording. The historical rela- 
tions of facts which we meet with, are by no 
means accurate delineations ; they change their 
aspect in the brain of the historian, they bend 
to his interest, and are tinctured by his preju- 
dices. What historian ever brought his reader 
to the scene of action, and laid the event cir 
cumstantially as it happened ? Ignorance and 
partiality disguise every thing. How easy it is 
to give a thousand varied appearances to the 
same facts, merely by a difference in the repre- 
sentation of circumstances. Exhibit an object 
in different points of view, and we scarcely be- 
lieve it to be the same, and yet nothing is 
changed, except the eye of the spectator. How 
often has it happened that a few trees, a hill on 
<he right or left, or a sudden cloud of dust, 



34-i TH E YOUNG MECHANIC. 

have turned the scale of victory, without the 
cause first being perceived ? Nevertheless the 
historian will assign a reason for the victory or 
defeat with as much confidence as if he had 
been at the same instant in every part of the 
battle. The worst historians, for a young 
reader, are those who favour us with their judg- 
ment. A plain narrative of facts is all he wants : 
let him judge for himself, and he will learn to 
know mankind. If he be constantly guided by 
an author's opinion, he sees only with the eyes 
of another; and when these are taken from 
him he does not see at all. History is generally 
defective in recording only those facts which 
are rendered conspicuous by name, place, or 
date ; but the slow progressive causes of those 
facts, not being thus distinguished, remain for 
ever unknown. A madness for party having 
possession of them all, they never endeavour 
to see things as they really are, but as they 
best agree with their favourite hypotheses.* 

It is the business of history to distinguish 
between the miraculous and marvellous; to 
reject the first in all narrations merely profane 
and human ; to scruple the second ; and when 

* Rousseau, b. iv 



HISTORY. 340 

obliged by undoubted testimony to admit of 
something extraordinary, to receive as little of 
it as is consistent with the known fans an* 1 
circumstances.* 

In undertaking a course of history, it is cer- 
tainly of great advantage to follow the chrono- 
logical order of events. Yon have then the 
gradual progress of man from barbarism to 
refinement; from refinement to corruption, ve- 
nality, and slavery ; from slavery back again to 
darkness and ignorance; and from this state 
again to knowledge, civilization, and liberty 
The most ancient history, except the Bible, is 
Herodotus ; and no history was ever more de- 
lightful for its simplicity, perspicuity, the un- 
affected style of the narrative, and easy and 
harmonious flow of the language. Mr. Beloe's 
translation, though not elegant, partakes in some 
measure, of the simplicity of the original. The 
history of Thucydides takes not so wide a 
scope as that of Herodotus, but the period 
which he describes is interesting, and his man- 
ner is incomparable. Smith's translation is 
tolerably good, and even that of Hobbes may 
be read without disgust. A more connected 

* Hume. 



346 TIIE YOUNG MECHANIC 

view of ancient history may be learnt from 
Rollin. The Ancient Universal History is an 
excellent and elaborate compilation, but it is 
tedious, and the style is dry and inharmonious : 
it is a book therefore rather for reference than 
study. The indefatigable Dr. Mavor has pro- 
duced an abridgment of this work, with addi 
tions, to the year 1802, in 25 volumes, 18mo 
Of the Roman historians there is a deplorable 
dearth of good translations. The order in 
which they may be read is Livy, Sallust, Caesar. 
The Epistles of Cicero are chiefly historical, 
which are admirably translated by Mr. Mel- 
moth. Plutarch's Lives should be read imme- 
diately after the Greek and Latin historians, or 
rather in conjunction with them : a good trans- 
lation has been done by the brothers Lang- 
horne. Of modern works, Vertot's Roman 
Revolutions, Montesquieu's Greatness and De- 
cline of the Romans, and Dr. Middleton's in- 
comparable Life of Cicero, may be read with 
the ancient historians. The last is a produc- 
tion of original genius, and yet comprises all 
which is most excellent in the writings of the 
great man whose life it narrates. The Anabasis 
of Xenophon, and the history of Poly bi us are 
most interesting and engaging books ; of the 



HISTORY. 347 

latter there is a translation by Hampton. Of 
the English compilations which contain the 
Iiistory of the Roman commonwealth, Fergu- 
son's is preferable to Hook's. Suetonius's His- 
tory of the Twelve Caesars is an ill-written 
book, yet it contains facts which are not to be 
found in any other original author. Tacitus is 
a treasure, not merely on account of the his- 
torical matter which it contains, but for the 
mass of moral instruction which it conveys. 
Murphy's translation may be pronounced supe- 
rior to Gordon's. After finishing Tacitus, we 
must, of necessity, have recourse to compila- 
tion. Mr. Gibbon takes up the subject where 
Tacitus left it, and certainly a nobler monu- 
ment of genius was never erected, than the 
" Decline and Fall of the Roman Empire ;" a 
narrative which extends to so modern a period, 
that a few books will serve to unite the chain 
of history with that of our own country. Dr. 
Robertson's Charles the Fifth is perhaps the 
most perfect historical composition in the En- 
glish language; and Dr. Watson's history is 
weii connected with it; both of which relate 
i<> some of the most important events recorded 
in history, the reformation of religion, and the 
establishment of the Batavian republic. Mr. 

no 



348 THE VOUNG MECHANIC 

Wraxall has filled up a chasm on the historical 
shelf, by his agreeable history of France; yet 
the student should not satisfy himself with that 
author's account of the age of Henry the Great, 
but inspect for himself the interesting and un- 
blemished pages of Sully ; and there are few 
scholars who will not find exquisite pleasure in 
the general history of the correct De Thou 
Yertot's Revolutions of Sweden and of Portu- 
gal, are both of them animated narratives of 
important events. Voltaire's Age of Louis the 
fourteenth and fifteenth, may be classed among 
original histories, though not of the first rank ; 
his Charles the Twelfth borders much on the 
romance. Dr. Robertson's History of America 
is a much admired composition. After such a 
course of reading, the student will not be ill 
prepared for the history of his own country. 
Hume's History is a bad compilation. Hume 
is, moreover, the avowed enemy of the two 
principles which conduce most to the happiness 
of mankind, leligion ana liberty; and he who 
makes hir.i the standard of his historical faith, 
will embrace numerous errors, arising not 
merely from design but from negligence. As a 
general history, Rapin's is preferable ; and if 
the state papers be passed over, it will not be 



HISTORY. 349 

bund more voluminous than Hume. Perhaps 
better course of English historical reading 
would be to take Dr. Henry's History for the 
early periods ; from the conclusion of which 
he may proceed with Rapin to the date of Cla- 
rendon's History ; and, for the affairs of Scot- 
land, having recourse to the classical narrative 
of George Buchannan, and the elegant history 
of Queen Mary, by the accomplished Robert- 
son. Clarendon's History, with his life, are 
invaluable records ; but his statements will, in 
some instances, be corrected by Whitlock's 
Memorials, which every student of history 
ought to read, and by the plain and manly, but 
interesting Memoirs of the ill-treated Ludlow. 
Though Bishop Burnet's egotisms have been 
ridiculed by Pope, Arbuthnot and Swift, yet he 
will continue to be read by every one who 
wishes to inform himself correctly of the man- 
ners and circumstances of the times in which 
that excellent prelate and really candid writer 
lived. Mrs. Macaulay's history evidently fa- 
vours republicanism, but her narrative is pure, 
and she is scrupulously exact in producing evi- 
dence and authority for all her facts. 

The student of history should always read 
with a map of the country before him. A good 



350 THE YOUNG MECHANIC. 

Biographical Dictionary is also an useful corn* 
panion in the study of history. Various plans 
have been recommended for connecting history 
with chronology in the mind ; the best method 
is perhaps to endeavour to fix in the memory 
the dates of some of the most remarkable events. 
The intermediate transactions will generally be 
found to have some link of association with 
the great events, and it will not be difficult to 
decide nearly on the date of any of them. 
There is, however, no better aid to the memo- 
ry than Dr. Priestley's Historical Chart.* 

On English History, the late Earl of Chatham 
thus wrote to his nephew. " If you have 
finished the abridgment of English History 
and of Burnet's History of the Reformation, I 
recommend to you next, before any other read- 
ing of history, Oldcastle's Remarks on the His- 
tory of England, by Lord Bolingbroke. Let 
me apprise you of one thing before you read 
them, and that is, that the author has bent some 
passages to make them invidious parallels to 
the times he wrote in ; therefore be aware of 
that, and depend, in general, on finding the 
truest constitutional doctrines; and that the 

•Mon. Mas. May, 1797. 



HISTORY. 35 

facts of history, though warped, are no where 
falsified. I also recommend Nathaniel Bacon's 
Historical and F olitical Observations ; it is 
without exception, the best and most instruc- 
tive book we have on matters of that kind 
They are both to be read with attention, ana 
twice over ; Oldcastle s Remarks to be studied 
and almost got by heart, for the inimitable 
beauty of the style, as well as the matter. Ba- 
con for the matter chiefly, the style being un- 
couth, but the expression forcible and striking. 

" I desired you sometime since to read Cla- 
rendon's History of the Civil Wars. I have 
lately read a much honester and more instruc- 
tive book, of the same period of history; it is 
the History of the Parliament, by Thomas 
May, Esq. If you have not read Burnet's His- 
tory of his Own Times, 1 beg you will. 

" I suppose you are going through the bio- 
graphers, from Edward the Fourth downwards, 
nor intending to stop till you reach to the con- 
tinuator of honest Kapin. There is a little 
book which 1 never mentioned, Wei wood's Me- 
moirs ; I recommend it. Davis's Ireland must 
not on any account be omitted ; it is a great 
performance, a masterly work, and contains 
much depth and extensive knowledge in state 



352 THE YOUNG MECHANIC. 

matters, and settling of countries, in a very 
short compass. I have met with a scheme of 
chronology by Blair, showing all contemporaiy 
historical characters, through all ages : it is of 
great use to consult frequently, in order to fir 
periods, and throw collateral light upon any- 
particular branch you are reading.*" 1 * 

Such is the recommendation of i hatham, a 
first rate authority. 

Among the historical works produced in our 
own country, Bancroft's History of the United 
States, 3 vols. 8vo., is entertaining and carefully 
written ; but it only brings the history down to a 
period shortly before the commencement of the 
Revolution. Frost's History of the United 
States, written for schools, brings it down to 
the year 1836. Prescott's Ferdinand and Isa- 
bella, and Irving's Columbus are delightful to 
read, and of the highest authority. 

BIOGRAPHY. 

Biography is a highly important branch of 
history. The biographer, by his accurate re- 
searches, supplies the deficiencies of the histo- 
rian. What the latter gives us only in outlines 

* Letters, passim. 



BIOGRAPHY. 353 

and sketches, the former presents in more com- 
plete and highly finished portraits. Their pro- 
vince does not merely extend to those who 
have acted upon the great theatre of the world, 
as sovereigns, statesmen, and warriors ; but to 
all who have improved human life by theii 
useful discoveries, adorned it by their works 
of genius, and edified mankind by their exam- 
ples. With what pleasure do we select a Ba- 
con, a Boyle, a Newton, an Addison, a Locke, 
a RadclifTe, a Howard and a Hanway, from the 
multitudes which surround them, and become 
acquainted with their particular characters and 
conduct ! To contemplate such men, not in- 
flamed by vain ambition, or courting empty 
popularity, but seeking retirement, and giving 
dignity to the walks of private life by the efforts 
of genius, and the exertions of philanthropy, 
is a high gratification to the mind, and inspires 
it witli an admiration and a love of those vir- 
tues, which come within the reach of general 
imitation. 

No species of writing gives a more perfect 
insight into the minds of men, than their let- 
ters. We observe them as they thought in their 
retired moments, when, withdrawn from the 
bustle of the world, they o ave free scope to 



354 T,IE YOUNG MECHANIC. 

their unrestrained opinions, and poured them 
without reserve, into the bosom of their friends. 
Among the numerous instances, which might 
be selected of epistolary excellence, we distin- 
guish the letters of Cicero, which display the 
sentiments of a vigorous mind, and give an in- 
sight into the eminent characters of his event- 
ful times. Pliny, in letters remarkable for neat- 
ness and precision of thought, expresses the 
dictates of a cultivated and generous mind. If 
we turn our attention to the epistolary litera- 
ture of our own country, we shall find that the 
piety and affection of Lady Russel, the quaint- 
ness and pleasantry of Howel, the manliness 
and political sagacity of Stafford, the philoso- 
phical exactness and cool judgment of Locke, 
the simplicity of Rundle, the moralizing vein 
of Johnson, and the taste and elegance of Gray, 
mark their respective letters with the strongest 
characters of originality, and give us the most 
pleasing pictures of their minds.* 

Besides the names above enumerated by Mr. 
Kett, the following may be added, as justly 
celebrated letter writers, viz. : Pope, Swift, Ad 
dison, Steele, Arbuthnot, Gay, Shenstone, Sterne, 

• Mr. Rett's Elements. 



BIOGRAPHY. 35,% 

Lyttleton, Lady Mary Wortley Montague, Rich- 
ardson, Chesterfield, Cowper, Sevigny, Mainte 
non, Burns, Lord Byron, and Horace Walpole 
Biography is, in general, a most pleasing as 
well as instructive branch of literature. When 
faithfully written it unveils man to man ; dis- 
covers the virtues and vices, the nobleness and 
meanness of which he is capable; and shows 
how the original sameness of human nature is 
varied by the operation of external causes into 
ten thousand different shapes, and assumes as 
many shades and hues. Man. to be known, 
must be viewed in every situation ; and when- 
ever he is fairly exhibited, whatever may have 
been his rank, station, or circumstances of birth 
or fortune, a valuable addition is made to sci 
ence. Whether the record respects the strug- 
gles of talents and worth through the chilling 
regions of obscurity and penury, up to the 
glittering eminences of fame and reward ; or 
whether it details the operations of pride and 
ambition on minds born to wealth and power; 
it presents an useful lesson, which those who 
are disposed to exertion and virtue will nol 
lead in vain.* 



* Mon. Rev. 
30* 



356 TIIE YOUNG MECHANIC. 

J would begin the study of the human heart, 
says Rousseau, by reading the lives of particu- 
lar men ; for there the hero conceals not him- 
self for a moment. The biographer pursues 
him into the most secret recesses, and exposes 
him to the piercing eye of the spectator ; he is 
best known when he believes himself most 
concealed. I confess the genius of a people is 
very different from that of man considered as 
an individual, and that we shall be imperfectly 
acquainted with mankind if we neglect the 
study of the multitude ; but it is also true, that 
we must begin by studying man in order to 
know mankind ; and that if we know the pro- 
pensities of each individual it will not be diffi- 
cult to foresee their effects when combined in 
the body of the people. The lives of kings 
may be written and rewritten, but we shall 
never see another Suetonius. Plutarch's excel- 
lence consists chiefly in those very minutiae 
into which we dare not enter. There is an 
inimitable gracefulness in his manner of paint- 
ing great men engaged in trivial employments, 
ard he is so happy in the choice of his inci- 
dents, that frequently a single word, a smile, a 
gesture, is sufficient to characterize his hero. 
Marshal Turenne was incontestably oj»e of the 



BIOGRAPHY. 357 

greatest men of the age in which he lived. The 
writer of his life has had the resolution to ren- 
der it interesting by relating some minute par 
ticulars which make his hero known and be 
loved ; but how many was he obliged to sup- 
press, which would have taught us Co know 
and love him still more! I shall instance one 
which I had from good authority, and which 
Plutarch would by no means have omitted, but 
which Ramsay, if he had known it, would not 
have dared to relate. The Marshal happened, 
one hot day, to be looking out at the window 
of his anlichamber in a white waistcoat and 
night cap. A servant entering the room, was 
deceived by his dress, and mistook him for one 
of his under cooks. He crept softly behind 
him, and gave him a violent slap on the breech. 
The Marshal instantly turned about, and the 
fellow, frightened out of his senses, beheld the 
face of his master : down he fell on his knees. 
" Oh ! my lord ! I thought it was George !" 
" And suppose it had been George," replied 
the Marshal, rubbing his back, " you ought 
not to have struck quite so hard." There are 
few people capable of conceiving the effect 
which reading, thus directed, would have on 
young minds. 



53 T1IJ3 YOUNG MECHANIC. 

The i% American Biography" of Mr Sparks, 
in ten volumes, is a work of great merit. It 
foims a part of Harper's School Library in 
which may be found many other biographical 
works jf our own countrymen as well as o/ 
distinguished foreigner*. 



ACCOMPLISHMENTS IN GENERAL 359 

CHAPTER XIII. 
THE MECHANIC'S STUDIES CONTINUED 

ACCOMPLISHMENTS IN GENERAL. 

A proper degree of attention should always 
oe paid to what are called the accomplishments 
of life, but they should never supersede for a 
moment more useful studies. Every occupa- 
tion should be estimated according to its future 
utility, and as those points which are deemed 
essential to the demeanour of a gentleman 
should not be neglected, and demand but a 
small portion of time to acquire, a pupil should 
be early and properly attended by the best 
masters in the several departments of drawing, 
music, horsemanship, and dancing. These ac- 
complishments, and the art of swimming, give 
a suppleness to the limbs, a grace of action, 
and an elegance of address and fine taste 
which always obtain the favourable preposses- 
sion of the company to whom a person may 
be introduced ; but talents and virtues complete 
the conquest of affection, and convert the pass- 



360 THE YOUNG MECHANIC. 

mg applause of the human race into a solid and 
durable esteem. 

A copious selection, says Mr. Yorke, from 
the excellent letters of Lord Chesterfield to his 
son, are always before my pupil, which inspire 
him with a laudable desire of uniting to the 
character of a man of knowledge, the accom- 
plishments of a gentleman. The object of in- 
struction is to make men better, not to embrute 
them. Whatever, therefore, is deemed auxiliary 
to such a disposition, should be encouraged. 
No evil can arise from an easy address, or from 
agreeable manners. Politeness is the handmaid 
of civilization ; perhaps it may be shown to be 
the attendant on virtue. Whatever means, 
therefore, are judged expedient to furnish the 
opportunity of exhibiting this amiable quality, 
are commendable, and ought to be adopted. ] 
allude, in this instance, to genuine politeness, 
not to that false affectation of good manners, 
which consists in foppery and a servile imitation 
of die servile manners of the great, and of men 
of honour, as, by a strange perversion of lan- 
guage, they are improperly called. The term 
great man, is so equivocal, says Dr. Beattie, 
that I will have nothing to do with it. The 
yilest scoundrel on earth, if possessed of a 



ACCOMPLISHMENTS IN GENERAL. 3(3 \ 

crown or a title, immediately commences great 
man, when he has with impunity perpetrated 
any extraordinary act of wickedness ; murder- 
ed fifty thousand men, robbed all the houses in 
half a dozen provinces, or dexterously plun- 
dered his own country to defray the expense 
of a ruinous war, formed to satiate his avarice. 
The term honour is also of dubious import. 
According to the notions of the present times, 
a man may sell his country, murder his friend, 
pick the pocket of his fellow sharper, and em- 
ploy his whole life in seducing others to vice 
and perdition, and yet be accounted a man of 
honour; provided he be accustomed to speak 
certain words, wear certain clothes, and haunt 
certain company. To the pernicious influence 
of this unnatural law of honour the just senti- 
ments of Archdeacon Paley may be applied. 
tt It is a law," says he, " which, being consti- 
tuted by men occupied in the pursuit of plea- 
sure, and for the mutual convenience of such 
men, will be found, as might be expected from 
the character and design of the law makers, to 
be, in most instances, favourable to the licen- 
tious indulgence of the natural passions. Thus ; 
it allows of fornication, adultery, drunkenness, 
prodigality, duelling, and revenge in the *x- 



3(}2 THE YOUNG MECHANIC. 

treme ; and lays no stress upon the virtues op- 
posite to these." 

If any additional supports were necessary in 
behalf of the argument that bodily accom- 
plishments may be considered as a component 
part of the happiness and perfection of man, 
we might introduce the powerful authorities of 
Mr. Locke and Dr. Watts, who have applauded 
this mode of instruction, when limited to such 
views. The latter was a man of singular piety, 
modesty, and uprightness ; the former was as 
much distinguished for the elegance of his 
manners, as for his knowledge of the world, 
and his deep insight into the powers of the 
human mind. 

TASTE. 

Taste is that power, which the mind pos^ 

sesses, of relishing the beauties found in the 

works of nature and art. 

Say what is Taste, but the internal powers, 
Active and strong, and feelingly alive 
To each fine impulse 1 a discerning sense, 
Of decent and sublime, with quick disgust 
From th : lgs deform'd. 

It has been alleged that Taste is a natural talent 
as independent of art as strong eyes, or a deb 



TASTE. 363 

cate sense of smelling ; and, without all doubt, 
the principal ingredient in the composition of 
taste is a natural sensibility, without which it 
cannot exist; but it differs from the senses in 
this particular, that they are finished by nature ; 
whereas taste cannot be brought to perfection 
without proper cultivation : for taste pretends 
to judge not only of nature, but also of art; 
and that judgment is founded upon observation 
and comparison. 

Though nature should have done her part, 
by implanting the seeds of taste, great pains must 
be taken, and great skill exerted, in raising 
them to a proper pitch of vegetation. The 
judicious tutor must gradually and tenderly 
unfold the mental faculties of the youth com- 
mitted to his charge. He must cherish his 
delicate perception ; store his mind with proper 
ideas ; point out the different channels of ob- 
servation ; teach him to compare objects ; to 
establish the limits of right and wrong, of truth 
and falsehood ; to distinguish beauty from tin- 
sel, and grace from affcctatioa \ in a word, to 
Strengthen and improve by culture, experience, 
and instruction, those natural powers of sensi- 
bility and sagacity, which constitute the faculty 
31 



361 THE YC TJNG MECHANIC 

called taste, and enable the possessor to enjoy 
the delights of elegant learning.* 

I do not call taste a species of judgment, 
although it be actually that part of judgment, 
whose objects are the sublime, beautiful and 
affecting; because this kind of judgment is not 
the result of reason and comparison, like a 
mathematical inference, but is perceived instan- 
taneously, and obtruded on the mind, like sweet 
and bitter on the sense, from which analogy it 
has borrowed the name of taste.f 

Taste presides with supreme authority over 
all the elegant arts. There are none so low in 
their subserviency to the uses of mankind, as 
not to afford subjects for its decisions. It ex- 
tends its influence to dress, furniture, and equip- 
age ; but presides, as in its most distinguished 
and eminent provinces, over poetry, eloquence, 
painting, architecture, sculpture, and music ; 
because among them genius takes its unbound- 
ed range, and exerts its fullest power. Taste 
is derived from the concurrent voices of men 
of various ages and nations, possessed of en- 
larged and cultivated understandings, who have 
iurveyed the works of genius with close atten 

* Goldsmith. -J- Usher's Clio. 



TASTE. 36 5 

tion, and have recorded in animated descriptions 
the impressions made upon their minds. This 
authority has stamped its approbation upon 
works which have obtained the general ap- 
plause of all ages and countries, and must still 
continue to produce a similar effect, so long as 
the intellectual powers of man remain the same ; 
so long as his imagination and sensibility are 
capable of being affected by all which is beau 
tiful, pathethic and sublime. 

The advance of national taste is similar to 
the progress of taste from childhood to man- 
hood. When the attention of an unpolished 
people is first directed to works of art, they are 
captivated by mere novelty ; and the rudest 
paintings and most unpolished verses obtain 
their applause. In proportion as superior efforts 
of genius are made, the opinion of the judi- 
cious part of the public, at least, becomes 
more correct; and what at first delighted is 
finally rejected with disapprobation. As soon 
as comparisons are made between different pro- 
ductions of the same kind, true taste is brought 
into action, its decisions are called for, and the 
justness of its discriminations is universally 
acknowledged. The polished contemporaries 
of Horace blushed at the praises which then 



3R6 



THE YOUNG MECHANIC. 



ancestors had bestowed on the rude dialogues 
of Plautus, and were charmed with the polite 
and elegant comedies of Terence. 

The lower orders of society are disqualified 
from deciding on the merits of the fine arts ; 
and the department of taste is consequently 
confined to persons enlightened by education, 
and conversant with the world, whose views 
of nature, art, and mankind, are enlarged by an 
extensive range of observation, and elevated far 
above gross ignorance ^and vulgar prejudice.* 

The general rudiments of taste are to be ac- 
quired first by reading books, which treat pro- 
fessedly on the subject. Secondly, by select- 
ing and explaining beautiful passages in Shaks- 
peare, Johnson, Sterne, Sec. And lastly, by exhi- 
biting and explaining prints of beautiful objects, 
or casts of the best antique gems and meda- 
lions. Authors have divided the objects of 
taste into the sublime, the beautiful, and the 
new; but another sect of inquirers into this 
subject have lately added the picturesque ; 
which is supposed to differ from the beautiful 
by its want of smoothness, and from the 
sublime, from its want of size.f 

♦ Mr. H. KetL 

f See Essay on the Picturesque, by U. Price, Es^. 



TASTE. ^g") 

Others have endeavoured to make a distinc 
lion between beauty and grace, and have e» 
teemed them a kind of rivals for the possession 
of the human heart. By grace may be defined 
beauty in action ; for a sleeping beauty cannot 
be called graceful, in whatever attitude she may 
recline ; the muscles must be in action to pro 
duce a graceful attitude, and the limbs to pro- 
duce a graceful motion.* 

Taste, says Lord Kaimes, is one of our facu 1 
ties which is the slowest in its progress toward, 
maturity ; and yet may receive some improve 
ment during the course of domestic education 
Compare with your pupils two poems on the 
same subject, or two passages. Take the lead in 
pointing out beauties and blemishes, in the sim- 
plest manner. Aft^r s<? me time, let them take the 
lead under your correction. You cannot have a 
better book for that exercise than the Spectator. 
A pleasing vein of genteel humour runs through 
every one of Addison's papers, which like the 
sweet flavour of a hyacinth, constantly cheers, 
and never overpowers. Steele's papers, on the 
contrary, are little better than trash; there is 
scai cely a thought or sentiment which is w orthy 

• Dr. Darwin's Plan of Education. 

31* 



368 THE YOUNG MECHANIC 

to be transferred into a common-place book 
My pupil reads a few papers daily without a 
single observation on my part. After some 
time, I remark to him the difference of compo- 
sition, which, in the course of reading, becomes 
more and more apparent. The last step is to 
engage him in distinguishing the two authors. 
He at first made awkward attempts ; from fre- 
quent trials, he began to distinguish. Now he 
will almost in the first period cry, " Foh ! this 
is Steele, let us have no more of him." 

If we wish to be directed to authors, who 
were eminent for correctness of taste, we may 
select in painting Fresnoy, Vasari, and Rey- 
nolds ; in music, Burney ; in eloquence, Cicero 
and Quintilian ; and in poetry, Horace, Pope, 
Gray, and the Wartons. These were critics, 
who had the singular merit of teaching that art 
in which they were themselves distinguished ; 
and their own works are an example and an 
illustration of their rules.* 

It is no wonder that wholly uneducated people 
want elegance and taste. It is not from them 
that we are to seek the natural bias of the soul 
The necessaries of life, when they are to be 

' • Mr. H. Rett's Elements. 



DRAWING. 359 

procured by an individual for a wife and nume- 
rous young children are procured by vast la- 
bour and hardship. Labour requires strained, 
forced, and violent motions. This race of men 
walk not for pleasure, but to perform journeys 
of necessity. They take advantage therefore 
of bending the body forward, and assisting their 
motion by a sling with their arms. Their low 
station, their wants, and their drudgeries, give 
them a sordidness and ungenerosity of disposi- 
tion, together with a coarseness and nakedness 
of expression ; whence their motions and ad- 
dress are equally rude and ungraceful. This 
dishonoured state of man is the offspring of his 
wants, and of the miseries which yoke him 
down a slave to the globe which he tills, and 
depress together his mind and his body.* 

DRAWING. 

Drawing is not only an accomplishment the 
nost elegant, agreeable, and ornamental, but, at 
the same time that it is the foundation of paint- 
ing, is of the utmost utility to the sculptor., the 
civil and naval architect, the engraver, the en- 
gineer, the mathematician, and navigator. Il 

•Clio. 



370 TIIE ltfttJMI MECHANIC. 

also assists the gardener, the cabinet maker, tl* 
weaver, &c. In short, there is scarcely a branch 
of civil society which is not indebted to it, from 
the maker of the iron rails before our house, to 
the tea urn on our table. To it we are indebt- 
ed for representations of those elegant remains 
of antiquity which have contributed so much 
to the advancement of our knowledge of fine 
form. Volumes of verbal description will not 
convey so true an idea of an object, as the 
slightest outline. Hence the source of much 
of our knowledge in antiquity, of which Ian 
guage could convey no adequate idea. To be 
able on the spot to make a sketch of a fine 
building, beautiful prospect, or any curious pro- 
duction of nature or of art, is not only a very 
desirable and elegant accomplishment, but in 
the highest degree entertaining. To treasure 
up whatever may occur in our travels, either 
for future use or to illustrate conversation, to 
represent the deeds of former ages, to preserve 
the features of our most valued friends, lias 
made this art not only one of the highest em- 
bellishments of our nature, but the delight of 
all ages. The greatest writers have united to 
praise, and empires to encourage it. It has 
been in the highest degree morally useful \ and 



DRAWING. 37^ 

where it has flourished, conferred honour on 
the country.* 

It is impossible to judge accurately of the 
dimensions of bodies, unless we learn also to 
know their figures, and even to imitate those 
figures ; for this imitation is founded on nothing 
else but the rules of perspective, and we can- 
not estimate the extension of bodies by their 
appearance, unless we have some knowledge 
of those rules. Children, being great imitators, 
all attempt to design ; I will have my pupil, 
says Rousseau, cultivate that art; not so much 
for the art itself, as for the sake of giving him 
a good eye and a flexible hand. I will take 
care that he shall rarely imitate imitations. He 
should have before his eyes the original itself, 
and not the paper representing it. Thus he 
should design a house from a house, a tree from 
a tree, a man from a man, that he may be ac- 
customed to observe minutely and accurately 
the appearance of bcrdies, and not take false and 
artificial imitations for those which are true and 
genuine. I would even discourage him from 
endeavouring to trace any thing from memory, 
till by frequent and repeated observations, its 

* Mr. E. Dayes in Mr. Tilloch's Philosop . Mag. vol 
iiv. 219. 



372 TIIE YOUNG MELllANIC. 

figure should be strongly imprinted on his 
imagination ; lest he should otherwise, by sub* 
stituting some fantastic image instead of the 
real one, lose the knowledge of proportion, and 
a taste for the genuine beauties of nature. 

Tf my pupil wishes to become a painter, he 
does not commence his career by a dry study 
of lines ; he does not " imitate imitations ;" he 
paints from nature. At the same time, that he 
may not lose the advantages derived from the 
labours of past ages, he submits his productions 
to a master of the art, who may correct his 
errors and accelerate his improvement. So in 
electricity, chemistry, &c, he begins by experi- 
ment, under the eye of a master, and thence 
either deduces his own general rules, or con- 
firms those of others.* 

MUSIC. 

Music may be considered one of the most 
useful means which we possess of improving 
and cultivating the mind of man, and by far the 
most powerful in softening the heart, and ren- 
dering it susceptible of every fine and more 
malted sentiment. Nor can music be called 

* Northmore. 



music. 374 

merely an art calculated to please and delight 
he senses alone, for certainly its execution 
employs the mind much more than the body 
To instance the many surprising effects pro- 
duced by music over the minds of men, even 
the most rude and barbarous, would be super- 
fluous and impertinent. The delight which 
music imparts to the mind, can be enjoyed in 
every period of life, from the earliest infancy 
to the total decay of all vital powers. No art 
affording 10 much felicity and happiness can 
be so easily cultivated and attained. The in- 
fluence of this part of education over the mind 
of the female sex, must be, and certainly is, 
highly beneficial. Their hearts are hence in a 
particular manner cultivated and refined, and 
those sensations are exercised and strengthened 
in their bosoms, which render them peculiarly 
lovely and amiable. Many females, however, 
are entirely deprived of the advantages result- 
ing from this part of education. 

It is sincerely to be lamented and regretted, 
that the truly respectable sect of Quakers should 
forbid the cultivation and practice of music in 
their societies; and it is wonderful that the 
effects which already have resulted from this 
prohibition, have not yet convinced them of th» 



374 T1IE YOUNG MECHANIC. 

impropriety and pernicious tendency of theii 
unreasonable prejudice against music. Such 
indeed are the effects produced by the tota? 
neglect of this divine art among the society of 
Friends, that the tones of their voice in reading 
and public speaking are so harsh and discordant 
as scarcely to be endured by a person of a nice 
and delicate musical ear. The worship of the 
catholic church, and that of the quakers, are in 
this respect as opposite as possible. The 
catholics chant their worship, and its influence 
is thereby augmented. 

The bravery and independence of the Swiss 
*e universally known, and in no people, per- 
haps, is the influence of pathetic music so pow- 
erfully exerted. The inhabitants of many other 
mountainous countries afford striking examples 
of the same kind. No people are more pos- 
sessed of true independence of mind than the 
inhabitants of the Highlands of Scotland, and 
in no country are the softer sensibilities of the 
heart more cultivated and indulged. I have 
never yet known an instance of a person capa- 
ble of enjoying all the ecstacy of musical de- 
light whose heart was not warm, tender and 
benevolent.* 

* Dr. Cowan. 



DANCING. 375 

DANCING. 

The design of this accomplishment is to ob- 
tain a graceful carriage, and a pleasing address 
on all occasions. It has been said, that " no 
person can either sit, stand, or walk well, un- 
less he dances well." This is certainly carry- 
ing tJie matter too far. There are some who 
never so much as learned a step, who both sit, 
stand, and walk with more grace than some 
professed dancing masters. This art, however, 
frequently teaches young people to walk with 
firmness and ease, to enter a room gracefully, 
to incline the head or body, even when sitting 
and conversing, without any distortion ; and 
removes that awkward stiffness, which in 
country people who have not had the advan- 
tages of a good education, is so apparent. To 
obtain great perfection in this art, though it be 
necessary for professiona' performers, would be 
a shameful waste of time, which might be infi- 
nitely better employed in mental attainments. 

POLITENESS. 

■ 
There is a fascinating manner in the address 
of some people, which almostly instantly con- 
ciliates the good-will, and even the confidence 
32 



376 THE YOUNG MECHANIC. 

of their acquaintance. Machiavel in his hia 
tory of Castruccio Castricani observes, that his 
hero could assume such openness of counte- 
nance, that though he was known to be a man 
practised in every art of fraud and treachery, 
yet in a few minutes he gained the confidence 
of all whom he conversed with ; they went 
away satisfied of his good will towards them, 
and were betrayed to their ruin. This enviable 
address, which may be used for good purposes 
as well as bad ones, is difficult to analyse ; it 
may possibly consist simply in a countenance 
animated with pleasure at meeting and con- 
versing with our acquaintance ; and which dif- 
fuses cheerfulness by pleasurable contagion 
into the bosoms of others ; and thus interests 
them in our behalf. It is net the smile of flat- 
tery, nor the smile of self-approbation, nor the 
smile of habit, nor of levity ; but it is simply 
an expression of pleasure, which seems to arise 
at the sight of our acquaintance; and which 
persuades them, that they possess our love, for 
which they barter their own in return. How- 
ever this conciliating manner may have beer 
used, as above related, for bad purposes, it pro 
bably proceeded originally from friendliness 
*nd openness of heart, with cheerful benevo 



POLITENESS. 377 

lence \ and that in those, who have in process 
of time become bad characters, the appearance 
of those virtues has remained, after the reality 
of them lias vanished. What then is the method 
by which this enchantment of countenance can 
be taught? Certainly by instilling cheerfulness 
and benevolence into the minds of young peo- 
ple early in life, and at the same time an anima- 
tion of countenance in expressing them ; and 
though this pleasurable animation be at lirst 
only copied, it will in time have the appearance 
of being natural ; and will contribute to pro- 
duce, by association, the very cheerfulness and 
benevolence, which it at first only imitated. 
This is an observation to which those who have 
the care of young children should closely attend. 
Next to the winning manners above described, 
the art of pleasing in conversation seems to 
consist in two things ; one of them to hear 
welly and the other to speak well. The per- 
petual appearance of attention, and the varying 
expression of the countenance of the hearer to 
the sentiments or passion of the speaker, is a 
principal charm in conversation ; to be well 
heard and accurately understood encourages 
our companions to proceed with pleasure, what- 
ever may be the topics of their discourse. 



378 TIIE rouwa mechanic. 

To speak agreeably, m respect to manner 
consists in a voice clear, yet not loud ; soft, 
yet not plaintive ; with distinct articulation, and 
with graceful attitudes rather than with graceful 
actions ; as almost every kind of gesticulation 
is disagreeable. In respect to the matter, it 
should be such as coincides with the tastes or 
pursuits of those to whom the conversation is 
addressed. Hence it will appear that to hear 
well, and to speak well, requires an extensive 
knowledge of things, as well as of the tastes 
and pursuits of mankind ; and must therefore 
ultimately be the effect of a good education in 
general, rather than a particular article of it. 
There are, however, faults to be avoided, and 
cautions to be observed, which should be point- 
ed out to young people. Of these I shall men- 
tion, — 1. That whenever the thirst of shining 
in conversation seizes on the heart, the vanity 
of the speaker becomes apparent ; and we are 
disgusted with the manner, whatever may be 
the matter of the discourse. 2. That it is 
a. ways childish, and generally ridiculous, when 
young people boast of their follies, or when 
they accuse themselves of virtues. 3. They 
should be apprised, that there is danger in 
speaking ill even of a bad person ; both be* 



POLITENESS. 379 

cause they may have been misinformed, and 
because they should judge their neighbours 
with charity. A friend of mine was once asked 
how he could distinguish whether the lady, 
whom he meant to address, was good temper- 
ed, and gave this answer : " When any dubious 
accusation is brought in conversation against 
an absent person , if she always inclines to 
believe the worst side of the question, she is 
ill tempered." There are some nice distinc- 
tions on this subject of good nature in Lady 
Pennington's Advice to her Daughters, which 
are worth the attention of young ladies. 4 
Strong asseverations, or a kind of petty oaths, 
such as " upon my honour j" appealing to 
others for the truth of an affirmation ; an 
always wrong, because such strong expression 
derogate somewhat from the character of the 
speaker, as they intimate that a simple assertion 
may not be believed. 5. Loud laughter, or 
tittering in short shrieks, as practised by some 
ladies at cards, are reprehensible. Dignity of 
character always suffers by being violently 
agitated at trivial circumstances. 6. A uniform 
adherence to sincerity in conversation is of the 
first importance. No artificial polish ot man- 
ners can compensate for the apparent want of 
32* 



380 THE YOUNG MECHANIC 

this virtue, nor any acquirements of knowledge 
for the reality of such a want. Opinions 
should be given with exact truth, if given at 
all ; hut when the characters of others are con- 
cerned, they should be delivered with diffidence 
and modesty. Lastly, a marked disapprobation 
should always be shown to indecency, immo- 
rality, or irreligion. In the softer sex, so great is 
their power in meliorating the characters of men, 
that if profligacy, infidelity, and debauchery, 
were universally despised, the morals of the 
age would be entirely reformed. To these 
might be added many other observations from 
various writers, concerning a due respect in con- 
versation to superiors, good temper to equals, 
and condescension to inferiors ; but as young 
people are not expected to speak with the wis- 
dom, or precision of philosophers ; and as the 
careless cheerfulness of their conversation, with 
simplicity of manner, and with grace, ease, and 
vivacity natural to youth, supplies it with its 
principal charms, these should be particularly 
encouraged, as there are few artificial accom- 
plishments, which could compensate for the 
loss of them * 

• Dr. Darwin. 



MORALS 381 

CHAPTER XIV. 

THE MORALS OF THE MECHANIC. 

The only lesson of morality proper for 
children, and the most important to persons of 
all ages, is never to do an injury to any one 
Even the positive precept of doing good, if not 
made subordinate to this, is dangerous, false, 
and contradictory. Who is there who does no 
good ? All the world, even the vicious man, 
does good to one or other party : he will make 
one person happy at the expense of making a 
hundred miserable ; hence arise our calamities. 
The most sublime virtues are negative ; they 
are also the most difficult to put in practice, 
because they are attended with no ostentation, 
and are even above that pleasure so flattering 
to the heart of man, that of sending away others 
satisfied with our benevolence. Oh how much 
good must that man necessarily do his fellow 
creatures, if such a man there be, who never 
did any of them harm ! The injunction of 
doing no one harm, infers that of doing Uie 
least possible harm to the community in gene* 



3g2 THE YOUNG MECHANIC. 

ral ; for in a state of society the good of one 
man necessarily becomes the evil of another.* 

I think it might be proved, that the best pre- 
cepts of morality, inculcated even under the 
sanction of religious awe, are not of half the 
efficacy in the prevention of vice, as a taste for 
reading and science. Experience informs us 
how soon the principles of morality inculcated 
in childhood are forgotten, or accommodated to 
the prevailing customs of the world : but if a 
taste for science be acquired, the affections are 
then fixed upon a rational object ; there is no 
temptation to allure them from the path of vir- 
tue ; at least the most powerful of all incite- 
ments to criminal amusements is removed, the 
tediousness of life during the intervals of lei- 
sure.")" 

Plato has observed with great propriety, that 
the end of the education and instruction of 
youth as well as the end of government, is to 
make men better ; and that whoever departs 
from this rule, however meritorious he may 
otherwise appear to be in reality, deserves 
neither the esteem nor the approbation of the 
public. The greatest erudition is of no value, 

* Rousseau, b. 2. -j- Gregory's Essays. 



MORALS. 3Q^ 

if unattended with probity. Jt is worse, it is 
dangerous to the welfare and tranquillity of so- 
ciety Quintilian, in his admirable treatise, has 
laid it down as a rule in forming- a perfect orato 
that none but an upright man can merit that 
name, and therefore he asserts as a necessary 
qualification, that he should not only speak 
well, but also possess all the moral virtues. Mr, 
Justice Blackstone has wisely adopted a similar 
opinion in his introductory lecture on the study 
of the law, in which, after having enumerate '. 
all the qualities of the head, he adds to them 
those of the heart, as indispensably necessary 
to form a truly valuable English lawyer, a Hyde, 
a Hale, or a Talbot. And Dr. Blair has, with 
great elegance and propriety, suggested the same 
idea as a necessary ingredient in the character 
of a sublime -writer. But this just sentiment is 
not to be restricted to any particular profession 
or order of men. The knowledge and prac- 
tice of morality is the voice of nature, which 
is unbounded and universal : and however ex- 
pedient it may be in those whose stations in 
life, render them objects of imitation or esteem, 
to perform with the most rigid punctuality 
every moral duty, it must not be forgotten, that 
tlie conviction of the utility of the practice, 



3S4 THE YOUNG MECHANIC. 

should make it the common sense and common 
respect of all mankind. 

The general rules of morality are formed by 
a constant observation of the fitness and pro- 
priety of actions in other men. What is fit to 
be done, and what excites universal applause, 
not only calls forth our own approbation, but 
warms us into a spirit of imitation. What 
ought to be avoided, we discover in the general 
sentiment of detestation which attends the per- 
petration of crime. The propriety of the former 
and the deformity of the latter quickly excite 
our emulation or abhorrence. We soon esta- 
blish a general rule for the regulation of our 
conduct, which receives a full confirmation from 
the opinion of the rest of mankind. It is thus 
that the general rules of morality are formed. 
They are ultimately founded upon experience 
of what, in particular instances, our mora! 
faculties, our natural sense of merit and pro- 
priety, approve or disapprove of. We do not 
originally approve or condemn particular ac- 
tions ; because, upon examination, they appear 
to be agreeable or inconsistent with a certain 
general rule. The general rule, on the contrary, 
is formed by finding from experience that all 
.ctions of a certain kind, or circumstanced id 



MORALS. ^g£ 

certain manner, are approved or disapproved 
of. An amiable action, a respectable action 
a horrid action, are all of them actions which 
naturally excite for the person who performs 
them, the love, the respect, or the horror of the 
spectator. The general rules which determine 
what actions are, and what are not, the objects 
of each of those sentiments, can be formed no 
other way than by observing what actions ac- 
tually and in fact excite them. The regard to 
those general rules of conduct, is what is pro- 
perly called a sense of duty, a principle of the 
greatest consequence in human life, and the 
only principle by which the bulk of mankind 
are capable of directing their actions. Without 
this sacred regard to general rules, there is no 
man whose conduct can be so much depended 
upon. It is this which constitutes the most 
essential difference between a man of principle 
and honour, and a worthless fellow. The one 
adheres on all occasions, steadily and resolutely 
to his maxims, and preserves through the whole 
of his life, one even tenor of conduct. The 
other acts variously and accidentally, as humour 
inclination, or interest chances to be uppermost. 
On the most scrupulous observance of these 
rules of conduct, depends the very existence 



383 THE YOUNG MECHANIC 

and happiness of human society, which would 
crumble into nothing if mankind were not 
generally impressed with a reverence for them. 
Among the many fortuitous events which 
spring up daily in the world, opportunities of 
inculcating a moral lesson frequently present 
themselves ; and when the mind has habituated 
itself to inquiry and discrimination, it will 
insensibly acquire a considerable degree of 
acumen, which may hereafter be employed 
with great emolument. For as it developes its 
powers of reasoning, it will direct this habit to 
other purposes of life, and virtue will have so 
strengthened its seat in the understanding, that 
its principles will be both relished and admired 
when at a future period they are examined ab- 
stractedly. It is for this reason, we cannot too 
often, after having laid down a moral principle, 
proceed to explain it by a practical illustration. 
A very little industry will qualify any one for 
this undertaking. The same volubility of 
speech which is often admirably exerted to 
propagate the villanous reports of scandal, and 
to tear piecemeal the domestic happiness of 
others, may be diverted, by this means, to an 
honourable and useful end. 



RELIGION. 3§7 

RELIGION. 

Disbelief or distrust of the truth of Chris- 
tianity arises in different men from different 
causes. Some who have been much accustomed 
to foreign travel, and have beheld opposite re- 
ligions firmly established in different countries, 
on the contrary sides of the same mountain, or 
the neighbouring banks of the same river; and 
others who have learnt from the records of his- 
tory that various systems of faith have suc- 
cessively prevailed in the same country ; that 
they have been changed again arifl again within 
very short periods ; and that each in its day 
has been implicitly received, and has produced, 
or, if an occasion offered, could have produced 
its martyrs ; such persons are sometimes prone 
to form what they term the liberal conclusion, 
that all religions are alike. They assert that the 
Supreme Being has enabled mankind to disco- 
ver, by the reasoning faculty with which h( 
has endowed them, those plain precepts of mo- 
rality, the observance of which is the only 
service required by him ; and that the object 
of all religions, however they may be encum- 
bered with fanatical rites and doctrines, which, 
in e'-'erv country, the wise will inwardly re gartf 
33 



3S8 TIIE YOUNG MECHANIC. 

with contempt^ is to inculcate the obligation of 

those precepts. Or they boldly pronounce thai 
religion of every kind is superstition : in other 
words, that though certain modes of conduct 
ought to be followed, and others to be ex- 
ploded, from principles of honour, and for the 
good of society ; to deem men bound to act in 
any case with a reference to a supposed will of 
the Deity, if a Deity exists, is of all absurdities 
the grossest. Others again, who have addicted 
themselves to philosophical investigations, have 
become decided unbelievers. Not that philoso- 
phy is the en^my of religion. The former is 
the natural ally of the latter. An inquiry into 
the laws which God has prescribed to the hu- 
man mind, to organized bodies, and to inanimate 
matter, leads at every step to a new display of 
his power, wisdom and goodness. But men 
who pursue it without any aim or desire to 
apply it to its most important use, that of 
heightening their reverence for the great Creator 
by a nearer acquaintance with his glorious at- 
tributes, easily become absorbed in the contem- 
plation of second causes ; and, though they may 
admit the existence, learn to deny the superin- 
tending care of the First Cause, and his interfe- 
-ence with the course of the material or the 



RELIGION. 3Q9 

moral world. Others seek for refuge in unbelief, 
on the same principle on which many of the Jews 
did in the days of Christ ; who " loved dark- 
ness rather than light, because their deeds wei o 
evil, and would not come to the light lest their 
deeds should be reproved." Resolved to per- 
sist in the vicious practices which Christianity 
proscribes, they take pains to convince them- 
selves that the gospel is the production of fraud 
and delusion ; they catch eagerly at every ob- 
jection against it of every kind, and turn from 
whatever seems to make in its favour ; in the 
language of scripture, they wink purposely 
with their eyes lest they should see, and shut 
their ears lest they should hear, and harden 
their hearts lest they should believe. Others 
by degrees becoming altogether immersed in 
political, commercial, or professional business, 
or in a continued succession of dissipated 
amusements, proceed from the omission of the 
practices of religious duties to the disuse and 
disregard of religious considerations, and ulti- 
mately to the disbelief of revealed religion, if 
not of all religion. And lastly, disdain of think- 
ing with the vulgar, disgust at casual instances 
vi superstition, and difficulties as to particular 



390 TIIE YOUNG MECHANIC. 

dcctrines, occasionally contribute to lead me* 
to unbelief. 

Besides the confirmed unbelievers of each oi 
these descriptions, there are many persons who 
from various causes, advance only part of the 
way on the road to infidelity, and stop short at 
different stages of doubt and distrust. 

Concerning unbelievers and doubters of every 
class, one observation may almost universally 
be made with truth; that they are little ac- 
quainted with the nature of the Christian reli- 
gion, and still less with the evidence by which 
its truth is supported. 

Now those who question or deny the truth 
»f Christianity will yet recdijy admit, that if the 
Supreme Being has actually made a revealed 
communication of his will, and has unequivocal- 
ly addressed it to all mankind ; and if there ate 
facts connected with that revelation which are 
acknowledged even by its enemies, and which 
justly afford, independently of other evidence, 
a strong presumption of its reality ; those per- 
sons must be highly guilty, who, having suffi- 
cient abilities and opportunities for inquiry, re- 
fuse or neglect to examine into the validity of its 
pretensions; and to examine with fairncns, and 
vitb the attention which the subject demands 



RELIGION. 39 

Is it then a thing highly improbable in itself 
that the Creator of the world should have given 
a revelation to mankind, and at the period when 
Christianity first appealed ? If the present stage 
of existence is but a very small part of the 
whole duration of a human being; if this stage 
is designed for the purpose of trial and proba- 
tion, and is thus to fix the state of each indivi- 
dual for ever ; if men were in fact ignorant of 
the certainty of these momentous truths, and 
unable to ascertain it by unassisted reason ; if, 
for want of a knowledge of that certainty, they 
were become a prey to crimes and delusions, 
indulging themselves in every species of wick- 
edness, and worshipping stocks and stones, and 
personified vices, with absurd and abominable 
rites ; can it be improbable that He who had 
manifested his goodness in creating them, should 
add another proof of the same disposition by 
imparting to them the further light necessary 
to correct their wanderings, and to guide them 
steadily in the way to happiness ? 

They who are led by these or other consi- 
derations to regard a revelation as a tiling not 
improbable in itself, ought from that circum- 
stance to feel, and naturally will feel, a greater 
readiness to inquire into the evidence of any 
33* 



392 THE YOUNG MECHANIC. 

professed revelation which bears outward mark? 
of reality. They who deem the existence of a 
revelation highly improbable cannot affirm thai 
it is impossible; and ought consequently in a 
similar case to institute a similar inquiry. For 
an antecedent persuasion of the improbability 
of the Deity's acting in any particular mannei 
is no mo^e a reason for refusing to examine 
whether he has not acted thus, if existing facts 
afford strong presumptive evidence that he has, 
than it would be for refusing to believe that he 
has, if conclusive evidence were produced. 

The question then which remains to be an- 
swered is this. Are there any leading circum- 
stances attending Christianity, circumstances 
generally admitted, and resting on independent 
proofs, which seem scarcely capable of being 
accounted for on any supposition but on that 
of truth ; and consequently furnish so strong a 
presumption of its being a divine revelation as 
to render those who doubt, or deny it, not 
merely imprudent but criminal, if they do not 
seriously inquire into its evidence ? 

The following statement, I apprehend, will 
justify the answering of that questior decidedly 
in the affirmative. 

The Christian religion, whether true or false. 



RELIGION. ;J93 

had its origin i*i a country and nation held in 
proverbial contempt in almost every part of the 
known world. The author of the religion was 
not only a Jew, but of the lowest rank among 
the Jews. He is universally allowed to have 
been uninstructed in literature and philosophy. 
He employed, in propagating his doctrine, as- 
sistants who were also Jews, and of a station 
as obscure, and of minds as little cultivated by 
learning, as his own. The religion which they 
preached was of such a nature as to be gene- 
rally and unavoidably most obnoxious. It was 
avowedly intended to supersede and annihilate 
every other religion. It attacked not only the 
doctrines and ordinances of the Jews, which 
they regarded as having been appointed by God 
himself; but those inveterate prepossessions 
which were rooted no less firmly in their 
hearts ; pronouncing the abolition of the pecu- 
liar privileges of the Jewish race, and the free 
admission of the abhorred Samaritans and Gen- 
tiles to all the benefits of the new dispensation. 
It not only exasperated the Romans by brand- 
ing as impious and detestable those rites and 
institutions which they had received with im- 
plicit reverence from their remote ancestors; 
and deriding as vain fictions every object of 



391 THE YOUNG MECHANIC. 

their adoration, even all the tutelar} deities o\ 
their empire ; but it also touched their jealousy 
in the tenderest point, by suggesting a prospeci 
of the revolt of Judea, and holding forth to 
their imaginations a competitor of Caesar, and 
the portentous appearance of the long expected 
sovereign, whom fate had destined to arise in 
the east. The founder of Christianity had 
neither the favourable circumstances to turn to 
his advantage, of which other teachers of new 
religions have availed themselves ; nor did he 
resort to those methods of proceeding to which 
they owed their success. He did not, like Ma- 
homet, pay court to a particular set of men, or 
a particular sect ; nor, like him, artfully conci- 
liate persons of all the different religious per- 
suasions in the country, by adopting and incor- 
porating into his own system some of the prin- 
cipal of their respective tenets ; nor, like him, 
permit licentious indulgences and promise licen 
tious rewards to his followers ; nor, like him. 
direct the propagation of his doctrine by the 
sword. He did not confine his instructions to 
solitudes and obscure hamlets; but delivered 
them in the most public manner, in populous 
cities, in ths most frequented parts of Jerusalem 
itself. He did not rest his pretensions on any 



RELIGION. 395 

species of evidence of a secret nature, or in 
any respect not generally cognizable by his co- 
temporaries ; but appealed to professed miracles 
performed in the sight of multitudes, and of 
such a kind that every man could judge as to 
their reality. He was not permitted by the 
contempt or the supineness of his enemies to 
proceed unmolested in making proselytes ; but 
was actively opposed from the beginning by the 
priests and chief men of the national religion ; 
was repeatedly in danger of losing his life ; and 
after a short ministry of three years duration at 
the utmost, was delivered to the civil power, 
and crucified as a malefactor. Yet notwith- 
standing this event the progress of the religion 
continued. The disciples of Christ, though 
they could have no reason to expect better 
treatment than their master had received; 
though they expected, as they had been taught 
by him and professed to expect, nothing in the 
present life but troubles and persecutions, per- 
severed in preaching the same religion as he 
had taught, with this additional and extraordi- 
nary circumstance that their master, on the third 
day after his crucifix 'jn, had arisen from the 
dead : and encountered the severest punish- 
ments, and death itself, rather than cease from 



396 THE YOUNG MECHANIC. 

publishing and attesting doctrines and facts, 
which, if false, they could not but know to be 
so ; and from the preaching of which, if true, 
they could look for no present advantage. And 
from these humble beginnings, and by these 
unpromising methods, did Christianity make its 
way so successfully, that within three centuries 
from the first preaching of Christ, it penetrated 
to the remotest extremities of the Roman em- 
pire, and established itself on the ruins of every 
other religion which it found existing. 

When all these circumstances are considered, 
and they are such as unbelievers in general are 
ready to admit, it seems nearly impossible not 
to come to the following conclusion : — that a 
religion of such an origin, and avowedly aiming 
at such objects; a religion thus destitute of all 
worldly means of credit and support, thus pro- 
voking and experiencing every kind of worldly 
opposition, could scarcely ever have obtained 
belief and acceptation, if its pretensions had 
not been founded on irresistible truth ; and con- 
sequently, that its establishment under all these 
circumstances affords so very strong a presump- 
tion that it is true, as necessarily to render every 
competent judge to whom they are known, and 
who doubts or disbelieves Christianity, crimi- 



RELIGION. 397 

nal in the sight of God, if he does not carefully 
examine into the specific evidence by which 
that religion is supported. 

This is the conclusion to which it has been 
my object to lead by fair reasoning the candid 
reader, who distrusts or denies the truth of the 
Christian revelation. If this conclusion appears 
to him well established, he will naturally seek 
for a detailed account of the evidence of the 
Christian religion in treatises written professedly 
on the subject ; and will make himself acquaint- 
ed with the many striking internal proofs which 
it bears of its own authenticity, by a diligent 
and attentive study of the Scriptures. And let 
him conduct the whole of his investigations 
with that impartial spirit which is always essen- 
tial to the discovery of the truth, whatever be 
the subject under discussion ; guarding against 
the influence of former prepossessions, and 
former practices, with a degree of caution and 
solicitude proportioned to the supreme import 
ance of the inquiry in which he is engaged. 
[jet him be prepared " to do the will of God ;" 
and he will not fail, " to know concerning the 
doctrine whether it be of God." 

I would in the next place offer a few obser- 
vations to the consideration of those believers 



398 THE YOUNG MECHANIC. 

in Christianity, who contend that an exact ob- 
servance of all its precepts is more than is now 
required of them. 

This plea for deliberate deviations from the 
strictness of obedience, a plea which we more 
frequently hear obscurely intimated than expli- 
citly stated, appears, when unfolded, to resolve 
itself into the following assertions : — that if the 
generality of men would act in scrupulous con- 
formity to the precepts of Christianity, no in- 
dividual could be vindicated were he to conduct 
himself otherwise ; but that every man must 
take the world as it is, and consider what is 
practicable in the existing state of things : that 
if government, for example, cannot be carried 
on without a certain degree of deceit and cor- 
ruption, the politician is excusable who prac- 
tises it ; that if men in trade cannot maintain 
their station without using the same objection- 
able arts which are adopted by their competi- 
tors, the necessity of the case is a sufficient 
apology; that similar reasoning is applicable 
to every other profession; that extravagant and 
needless latitude would certainly be unjustifi- 
able ; but that it is absurd to require points of 
morality to be pushed to extremes, and to refusi 



RELIGION. 399 

to make necessary allowances for compliance 
with established customs. 

Before we examine what countenance the 
plea in question meets with in the Scriptures, 
it may be useful to inquire whether it approves 
itself to sober reason. 

Now, since they who allege this plea, pro- 
fessedly make the degree in which it is custo- 
mary for men to deviate from the rules pre- 
scribed in the Gospel, the standard measure of 
the degree of latitude in deviating from them 
which each individual is at liberty to use ; they 
must unavoidably admit, if they will reason con- 
sistently with their own principles, that when 
the general depravity is augmented in any pro- 
portion, exactly in the same proportion is that 
latitude augmented ; and consequently that a 
degree of latitude, which in one state of things 
they pronounce extravagant and unnecessary, 
may become highly needful and proper in 
another. This in fact is to affirm, that instead 
of the practice of men being rendered conform- 
able to the laws of God, the degree of obe- 
dience due from any man to those laws depends 
solely on the practice of his neighbours ; and 
that if it should be the general practice utterly 
to disregard and contemn them, no individual 



400 TIIE YOUNG MECHANIC. 

would be under any obligations to pay to them 
the slightest attention whatever. If an argu- 
ment like this, which strikes directly at the root 
of all religion, cannot be maintained by those 
who believe in Christianity ; neither can the 
plea which necessarily involves it. 

In the next place, does this plea receive more 
encouragement from the Scriptures ? From that 
quarter it experiences nothing but repulse and 
condemnation. Those who urge it cannot pro 
duce one single text authorizing an individual 
to relax in his obedience to the precepts of the 
Gospel, for the sake of escaping difficulties and 
losses, through fear of giving offence, through 
deference to custom or authority, or through 
any worldly motive whatever. What is the 
language of the Old and New Testaments on 
the subject ? " Thou shalt not follow a multi- 
tude to do evil." — " Be not conformed to this 
world," (that is, to the evil principles and prac- 
tises which prevail in it,) "but be transformed 
by the renewing of your mind, that ye iaay 
prove what is that good, and acceptable and 
-vrfcct will of God." — " Love rot the world, 
neither the things that are in the world. If any 
man love the world, the love of the Fathei is 
not in him For all that is in the world, the 



RELIGION. <0l 

lust of the flesh, and the lust of the eyes, and 
the pride of life, is not of the Father, but is of 
the world. And the world passeth away, and 
the lust thereof: but he that doeth the will of 
God abideth for ever." — " Be ye therefore per- 
fect, even as your Father which is in Heaven is 
perfect." — " The love of Christ constraineth 
us, because we thus judge, that if one died for 
all, then were all dead : and that he died for 
all, that they which live should henceforth not 
live unto themselves, but unto him which died 
for them and rose again." — " What shall it profit 
a man, if he shall gain the whole world, and 
lose his own soul ? Or what shall a man give 
in exchange for his soul ? Whosoever there- 
fore shall be ashamed of mo, and of my words, 
in this adulterous and sinful generation, of him 
also shall the Son of man be ashamed, when 
he cometh in the glory of his Father with the 
holy angels." To these passages are to be 
added the directions incidently given by St. Paul 
to persons in many different stations, exhorting 
them to fulfil the respective offices peculiar to 
those stations " for conscience sake, as unto the 
Lord, and not unto men ;" directions which, 
Dy parity of reasoning we may rest assured 
that the apostle would have applied to all other 



402 THE 10UNG MECHANIC. 

situations and circumstances of lifj, if he had 
been led by his subject to notice them distinctly 
And he did in fact make the application univer- 
sal, when he delivered these general and com- 
prehensive precepts : " Whatsoever ye do, do 
all to the glory of God." — " Whatever ye do, 
in word or in deed, do all in the name of the 
Lord Jesus." A serious desire to please God 
in all we do, rendering the manner of pursuing 
the business of our calling, be it what it may, 
one of the expressions of that desire, is the 
grand principle which these passages inculcate ; 
and it is the principle which, beyond all others, 
I could wish to impress on the mind of the 
reader, whatever be his station or profession, as 
being the only one which will lead him steadily 
to fix his attention on the duties which he has 
to perform, and the temptations which he must 
encounter. It is impossible to conceive that he 
who knowingly deviates from the path of moral 
rectitude and Christian duty, because most 
otheTs in the same rank and profession with 
himself deviate from it, and because, by forbear- 
ing to deviate, he should incur embarrassment 
and losses, odium and disgrace, is, in that in- 
stance, acting consistently with the letter or the 
spirit of the various scrptural injunctions which 



RELIGION. 403 

have been quoted. Let those who find them- 
selves tempted to such deviations, consider 
whether it is not probable that the Supreme 
Being, on whose providence the success of 
every undertaking depends, will prosper those 
who scrupulously observe the laws which he 
has prescribed for their conduct, and leave the 
issue in his hands, rather than those who mani- 
fest their distrust of his care by resorting to 
arts and practices which he has forbidden ; 
whether those who are injured in their worldly 
pro^pe^ts by their conscientious adherence to 
the line of rectitude, are not entitled to the full 
benefit of the scriptural consolation, tt If ye 
suffer for righteousness sake, happy are ye :" 
and whether it jg not the part of wisdom as 
well as of duty, whatever be the event at pre- 
sent, to regulate every action by that rule, ac- 
cording to which it will be judged at the l«sf 
day 



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